Fortunate Recall: Ontology-Driven Memory Lifecycle Management for Persistent Coherence in LLMs

# Ontology-Driven Memory Lifecycle Managementfor Persistent Coherence in LLMs
Source: [https://arxiv.org/html/2609.10413](https://arxiv.org/html/2609.10413)
## Fortunate Recall: Ontology\-Driven Memory Lifecycle Management for Persistent Coherence in LLMs

###### Abstract

Current LLM memory systems treat all personal facts identically, storing them in flat vector stores or knowledge graphs with uniform retention, so stores grow unboundedly while retrieval precision degrades\. The core challenge is lifecycle management: which memories should persist, which should be replaced, and at what rate, conditioned on the behavioral type of each fact\.Fortunate Recall\(FR\) is a composable policy layer that classifies personal facts into a 10\+1 behavioral ontology and applies category\-specific lifecycle policies \(differential temporal decay, slot\-key supersession, event\-time validity, and category\-aware retrieval routing\) as deterministic functions over LLM\-extracted metadata\. The lifecycle policy layer is pure math; the LLM is used at ingestion and for a single lightweight candidate\-selection step at retrieval\. FR\-Bank, our infrastructure\-independent implementation, achieves 76\.9% pass rate onLifecycleBench, a new 516\-question temporal\-disambiguation benchmark, outperforming Mem0 \(61%\), A\-MEM \(65\.3%\), Memory\-R1 \(66\.9%\), and MemoryOS \(70\.5%\) across seven system configurations, and reaches 75\.2% on the full 500\-question LongMemEval\-S benchmark under the canonical Wu et al\. \(ICLR 2025\) judge protocol, demonstrating that lifecycle policies impose no measurable aggregate cost on standard retrieval tasks\. A pre\-registered ablation locates where the gains originate\. Replacing the typed layer with three generic lifecycle primitives over a semantic\-only ranker leaves correctness statistically unchanged \(Δ=−1\.7\\Delta=\-1\.7pp, 95% CI\[−6\.0,\+2\.7\]\[\-6\.0,\+2\.7\], n\.s\.\), so the*generic lifecycle metadata*carries the correctness advantage; what the behavioral ontology carries is calibration, halving downstream confabulation \(12\.0% vs\. 24\.2% over all queries,p<0\.001p<0\.001\) by making per\-category parameterization feasible where no single global weight is\. End\-to\-end, FR\-Bank reduces confabulation from Mem0’s 45\.1% to 22\.4% over answered queries and from 32\.2% to 13\.0% over all 516 queries, while answering more of them correctly \(31\.2% vs\. 18\.6%\); the hierarchy replicates on the open\-weight Kimi K2\.5 generator, and upgrading Mem0’s extractor to gpt\-4\.1\-mini narrows the retrieval gap without touching its structural deficits on supersession and retraction\. The decomposition transfers toBEAM\(ICLR 2026\), a benchmark constructed independently of this work: 46\.8% correct vs\. Mem0’s 32\.9% over 280 questions, splitting into\+23\+23to\+26\+26from the generic metadata and\+10\+10to\+13\+13from the ontology, concentrated in contradiction resolution\. A six\-point granularity sweep places the ontology’s benefit on a plateau from roughly seven effective policy clusters, so 10\+1 is an interpretable point on that plateau rather than a uniquely necessary granularity\. The ontology, benchmark, and code are released as supplementary material and will be made publicly available upon publication\.

## 1Introduction

Large language models lose coherence over extended conversations because existing memory systems treat all personal facts uniformly\. A user’s ethnicity, current food preference, and six\-month\-old dentist appointment coexist in the same store with identical retrieval priority, yet their appropriate persistence dynamics differ by orders of magnitude\. The core challenge is not retrieval but*lifecycle management*: determining which memories should persist, which should be replaced, and at what rate, conditioned on the behavioral type of each fact\.

Building on early work on LLM agent memory\[[20](https://arxiv.org/html/2609.10413#bib.bib20)\], recent systems have established strong infrastructure: temporally\-aware knowledge graphs \(Zep/Graphiti\[[2](https://arxiv.org/html/2609.10413#bib.bib2)\]\), Zettelkasten organization \(A\-MEM\[[4](https://arxiv.org/html/2609.10413#bib.bib4)\]\), OS\-inspired hierarchies \(MemoryOS\[[9](https://arxiv.org/html/2609.10413#bib.bib9)\]\), RL\-learned operations \(Memory\-R1\[[10](https://arxiv.org/html/2609.10413#bib.bib10)\]\), and adaptive structure selection \(FluxMem\[[12](https://arxiv.org/html/2609.10413#bib.bib12)\]\)\. None distinguishes a current preference from a superseded one, recognizes expired logistics, or models an approaching deadline, and existing benchmarks\[[1](https://arxiv.org/html/2609.10413#bib.bib1)\]likewise do not measure whether a system can tell current from outdated state\.

We introduceFortunate Recall\(FR\), a composable lifecycle policy layer that classifies each extracted fact into one of 10\+1 behavioral categories \(Table[1](https://arxiv.org/html/2609.10413#S3.T1)\)—not cognitive types \(episodic/semantic/procedural\) but behavioral domains that directly determine temporal dynamics—and applies category\-specific decay, supersession, event\-time validity, and routing policies as deterministic functions\. Every retrieval decision is a named term of a single closed\-form log\-score, with no learned black box mediating lifecycle behavior, at a median47​μ​s47\\,\\mu\\mathrm\{s\}and empirically linearO⁡\(k\)O\(k\)scaling\.

Contributions\.\(1\) A behavioral ontology derived from how personal facts change over time, with per\-category deterministic lifecycle policies \(Table[1](https://arxiv.org/html/2609.10413#S3.T1)\)\. \(2\) A lifecycle non\-identifiability theorem with sufficiency, minimality, and individual\-necessity results for the metadata basis\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\); these are representation\-level results about the*basis*and do not claim the 10\+1 partition, the rates, or the pipeline are optimal \(§[4](https://arxiv.org/html/2609.10413#S4)scopes each claim\)\. \(3\)LifecycleBench, a 516\-question temporal\-disambiguation benchmark over 40 personas with 9 attack vectors, positioned as a dense lifecycle stress test rather than the first benchmark to touch temporal updates\. \(4\)FR\-Bank, the infrastructure\-independent reference implementation, at76\.9%76\.9\\%on LifecycleBench and75\.2%75\.2\\%on full LongMemEval\-S under the Wu et al\. protocol, with end\-to\-end validation across seven configurations and two generator families under both the answered\-query and all\-query denominators\. \(5\)An attribution and transfer studyseparating the stack’s two layers: a pre\-registered untyped ablation \(§[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)\), transfer to the independently built BEAM benchmark \(§[6\.6](https://arxiv.org/html/2609.10413#S6.SS6)\), a six\-point granularity sweep, a full metadata\-noise grid, and two machine audits of our own judge\. Ontology, benchmark, code, pre\-registration files, and raw per\-question judgments are released and will be made public upon publication\.

## 2Related Work and Gap Analysis

Existing systems exhibit complementary gaps, mapped feature by feature in Table[32](https://arxiv.org/html/2609.10413#A5.T32)\(Appendix[E](https://arxiv.org/html/2609.10413#A5)\); we summarize the pattern rather than enumerate it\. Flat vector stores \(Mem0\[[19](https://arxiv.org/html/2609.10413#bib.bib19)\]\) and dynamic organizers \(A\-MEM\[[4](https://arxiv.org/html/2609.10413#bib.bib4)\]\) provide no structured lifecycle\. Cognitive\-type categorizations \(MemoryOS\[[9](https://arxiv.org/html/2609.10413#bib.bib9)\], MIRIX\[[11](https://arxiv.org/html/2609.10413#bib.bib11)\]\) describe memory*form*rather than*behavior*: a chronic illness and a lunch order are both “semantic” yet need very different dynamics\. Memory\-R1\[[10](https://arxiv.org/html/2609.10413#bib.bib10)\]learns operations by RL over a flat \{ADD, UPDATE, DELETE\} space containing no expiry or retraction action, so its gap is vocabulary rather than optimization\. MemoryBank\[[5](https://arxiv.org/html/2609.10413#bib.bib5)\]applies Ebbinghaus\[[21](https://arxiv.org/html/2609.10413#bib.bib21)\]curves with one uniform decay for all fact types\. MemGPT\[[8](https://arxiv.org/html/2609.10413#bib.bib8)\]and, at query time, APEX\-MEM\[[17](https://arxiv.org/html/2609.10413#bib.bib17)\]delegate lifecycle decisions to LLM reasoning—expensive and opaque where FR’s policies are deterministic—and neither types facts, applies differential decay, or models event\-time validity\. Zep/Graphiti\[[2](https://arxiv.org/html/2609.10413#bib.bib2)\]offers production temporal knowledge graphs with no forgetting mechanism and only binary supersession; FluxMem\[[12](https://arxiv.org/html/2609.10413#bib.bib12)\]adapts memory*structure*rather than*policy*\. FR’s bi\-temporal representation parallels the valid\-time / transaction\-time distinction in temporal databases\[[16](https://arxiv.org/html/2609.10413#bib.bib16)\], extended with behavioral conditioning\.

Benchmarks\.LongMemEval\[[1](https://arxiv.org/html/2609.10413#bib.bib1)\]and LoCoMo\[[13](https://arxiv.org/html/2609.10413#bib.bib13)\]measure long\-horizon retrieval without testing whether a system distinguishes current from outdated state, and BEAM\[[14](https://arxiv.org/html/2609.10413#bib.bib14)\]spans ten memory abilities at contexts up to 10M tokens, several of them lifecycle\-sensitive\. We therefore position LifecycleBench not as the first benchmark to touch temporal updates or forgetting but as a*dense lifecycle stress test*, every question constructed so the correct answer depends on lifecycle state\. Since we introduce both benchmark and method, §[6\.6](https://arxiv.org/html/2609.10413#S6.SS6)transfers the same comparison onto BEAM, which we did not build\.

Distinction from cognitive typologies\.MemoryOS and MIRIX\[[11](https://arxiv.org/html/2609.10413#bib.bib11)\]categorize by cognitive type \(episodic/semantic/procedural\), which describes the*form*of memory\. Our ontology describes the*behavioral domain*: a parent’s chronic illness is “semantic” in cognitive typology but “Health & Wellbeing” in ours; a meeting time is also “semantic” but “Logistical Context\.” The cognitive type does not determine appropriate lifecycle dynamics; the behavioral domain does\.

## 3Fortunate Recall

![Refer to caption](https://arxiv.org/html/2609.10413v1/FINAL_FIGURE_1.png)Figure 1:Fortunate Recall architecture and the LLM / lifecycle\-math boundary\.*Ingestion*\(top, asynchronous\): onegpt\-4\.1\-minicall per turn extracts each edgeeeand tags it with behavioral categorycc, slot keyκ\\kappa, lifecycle stateξ\\xi, event\-time anchorhh, ingest timett, and confidencevv;ttandhhare two independent clocks \(bi\-temporal\)\.*Retrieval*\(bottom, per query\): hybrid candidate generation is distilled by a single small\-model call to top\-20, which the*deterministic lifecycle layer*ranks by the closed\-form log\-score of Eq\. \([2](https://arxiv.org/html/2609.10413#S4.E2)\)\. The pipeline uses exactly two LLM calls per turn, and every lifecycle decision is a named term ofℓ\\ell, inspectable per edge and per term at millisecond latency\.The architecture \(Figure[1](https://arxiv.org/html/2609.10413#S3.F1)\) comprises an infrastructure layer adopting established patterns \(bi\-temporal validity, hybrid retrieval\) and a lifecycle policy layer providing behavioral dynamics\.

### 3\.1The Behavioral Ontology

Each extracted fact is classified into one of 10\+1 behavioral categories \(Table[1](https://arxiv.org/html/2609.10413#S3.T1)\), by how it changes over time rather than by cognitive form\. The category determines the fact’s full lifecycle—decay rate, supersession semantics, expiry logic, and retrieval routing—so that a chronic illness and a lunch order, both “semantic” in cognitive typology, receive the policies their temporal behavior demands\.

Empirically grounded design\.An “identity gravity well” in our original 8\+1 design \(Identity absorbing∼\{\\sim\}38% of all facts\) motivated the three\-way split into Identity, Hobbies, and Preferences; emotional state is excluded as a category because mood modulates other categories rather than constituting a memory type\. Facts are soft\-clustered with membership weights summing to 1\.0, so the effective decay rate is the weighted harmonic mean of category\-specific rates \(Lemma 1; soft\-membership statistics, the granularity sweep, and the within\-category variance comparison are in Appendix[A\.5](https://arxiv.org/html/2609.10413#A1.SS5), with Figure[2](https://arxiv.org/html/2609.10413#A2.F2)in Appendix[B](https://arxiv.org/html/2609.10413#A2)illustrating supersession and event\-time validity end\-to\-end\)\.

Table 1:The 10\+1 behavioral ontology\. Each category determines lifecycle dynamics: decay rate \(half\-life\), supersession semantics, and expiry logic\. Half\-lives govern base decay; actual persistence also depends on access frequency and soft category membership \(Appendix[B](https://arxiv.org/html/2609.10413#A2)\)\.\#CategoryKey PolicyHalf\-lifeExample Transition1Identity & Self\-ConceptAccumulate; high\-confidence supersession19 days“Works at Google”→\\to“Joined Anthropic”2Relational BondsAccumulate; explicit dissolution19 days“Dating Alex”→\\to“Broke up with Alex”3Intellectual InterestsAccumulate; reactivatable14 daysDormant interest resurfaces after months4Health & WellbeingChronic: identity\-like; Acute: expire12 daysFlu resolves; diabetes persists5Projects & EndeavorsState machine: active/done/paused12 days“Writing thesis”→\\to“Thesis defended”6Hobbies & RecreationSlow decay; dormancy detection8 daysNo fishing mentions for 6 months7Preferences & HabitsSlot\-key supersession6 days“Likes pizza” superseded by “Likes sushi”8Financial & MaterialState tracking; supersession5 days“Rent $950/mo”→\\to“Rent $1,100/mo”9ObligationsEvent\-time validity; anticipatory5 daysDeadline activates as it approaches10Logistical ContextFastest decay; event\-time expiry4 days“Flight at 6am tomorrow”→\\toexpires11Other / Open\-SetModerate default10 daysFacts resisting classification

### 3\.2Classify the Fact, Not the Entity

Classification must target the*fact*\(the relational edge\), not the conversational utterance or the entity node\. Utterance\-level classification confuses the conversational frame with the information being memorized \(“I changed my last name while updating my insurance paperwork” is about Identity, not Obligations\)\. Entity\-level classification assigns wrong lifecycle policies to edges that happen to involve the same node \(“Alex caught 7 bass” should be Hobbies, not Relational just because Alex is a person\)\. Fact\-level classification ensures each edge receives its category based on what it represents\. A reproducible three\-judge classifier\-agreement audit \(κ=\+0\.67\\kappa=\+0\.67with full session context\) is in Appendix[B\.1\.1](https://arxiv.org/html/2609.10413#A2.SS1.SSS1)\.

### 3\.3Lifecycle Mechanisms

Differential temporal decay\.Each category has a base decay rateλc\\lambda\_\{c\}with activationa\(e\)=exp\(−λc⋅Δt\)a\(e\)=\\exp\(\-\\lambda\_\{c\}\\cdot\\Delta t\)\. Rates span a5\.3×5\.3\\timesrange from Identity \(slowest\) to Logistical \(fastest\), calibrated to prevent category hierarchy squatting \(Appendix[I](https://arxiv.org/html/2609.10413#A9)\)\.

Slot\-key supersession with confidence weighting\.For categories with*replace*semantics, normalized \(subject, attribute\) slot keys trigger supersession\. High\-confidence contradictions mark old edges inactive; low\-confidence cases preserve both values \(soft supersession\)\. “Thinking about moving to London” preserves “lives in Istanbul”; “moved to London” supersedes it \(Appendix[F](https://arxiv.org/html/2609.10413#A6)\)\.

Event\-time validity and anticipatory activation\.For Obligations and Logistics, activation is governed by distance to the event, not from creation\. Deadlines*increase*in activation as they approach, then expire after passing\. A date\-aware filter with backward\-looking bypass removes past\-date events before reranking\.

Category\-aware retrieval routing\.Query classification pulls per\-category candidate sets alongside global semantic candidates\.*Category\-forced retrieval*extends this: for the predicted category, all edges are retrieved \(up to 20\), bypassing vocabulary gaps between abstract queries and specific stored facts\.

### 3\.4Core Mechanism versus Implementation Engineering

FR\-Bank is a full retrieval stack, and not every part of it is a lifecycle mechanism\. Table[2](https://arxiv.org/html/2609.10413#S3.T2)separates the two\. The dividing line is measured rather than asserted: the “core mechanism” rows are exactly the components that the untyped lifecycle baseline of §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)retains or removes, so the measured difference between those two configurations is what isolates the classification layer’s contribution\.

Table 2:Core FR mechanisms versus implementation engineering\. Every engineering row is independently ablated; every core row is grounded in a theoretical result, a measured ablation, or both\.ComponentClassGroundingBehavioral classification \(cc\)CoreThm 3 \(§[A\.7\.1](https://arxiv.org/html/2609.10413#A1.SS7.SSS1)\); Thm 4 \(enables per\-category calibration\); measured: confabulation halved,\+\+CR on BEAMSlot\-key supersession \(κ,Ω\\kappa,\\Omega\)CoreThm 1 construction; Thm 3 \(§[A\.7\.2](https://arxiv.org/html/2609.10413#A1.SS7.SSS2)\)Lifecycle\-state mask \(ξ,Mq\\xi,M\_\{q\}\)CoreThm 3 \(§[A\.7\.3](https://arxiv.org/html/2609.10413#A1.SS7.SSS3)\); Thm 3′′Event\-time validity kernel \(h,Vch,V\_\{c\}\)CoreThm 3 \(§[A\.7\.4](https://arxiv.org/html/2609.10413#A1.SS7.SSS4)\); Thm 3′; Prop\. 2Category\-conditioned decay \(ScS\_\{c\}\)CoreModel 1; ablation\+6\+6pp \(Table[3](https://arxiv.org/html/2609.10413#S6.T3)\)Category\-aware routing \(ρ\\rho\)CoreAblation\+6\+6pp; scale\-emergent \(Appendix[N](https://arxiv.org/html/2609.10413#A14)\)Semantic floorsEngineeringAblated, Table[52](https://arxiv.org/html/2609.10413#A24.T52)\(Hit@131%→19%31\\%\\to 19\\%without\)Numeric rescueEngineeringAblated, Appendix[H](https://arxiv.org/html/2609.10413#A8)\(AV881%→94%81\\%\\to 94\\%\)LLM distillation stepEngineeringSubstrate\-level retrieval aid, Appendix[Z](https://arxiv.org/html/2609.10413#A26)Date filter\+\+backward\-looking bypassEngineeringAblated, Table[52](https://arxiv.org/html/2609.10413#A24.T52)BM25 hybrid\+\+per\-source normalizationEngineeringAppendix[Z](https://arxiv.org/html/2609.10413#A26)World\-knowledge filterEngineeringAppendix[Z](https://arxiv.org/html/2609.10413#A26)\(86%→1\.4%86\\%\\to 1\.4\\%contamination\)
### 3\.5The LLM Boundary

LLMs are used atingestionfor entity/edge extraction, behavioral classification, world\-knowledge detection, supersession detection, slot\-key and event\-time extraction, and emotional loading detection, and for asingle lightweight candidate\-selection step at retrieval\(gpt\-4\.1\-mini distillation that selects top\-20 from the merged semantic\+BM25\+category\-forced pool\)\. The lifecycle policy layer is pure deterministic math: category\-conditioned decay, supersession filtering, event\-time checking, category\-aware routing, and blended scoring all execute as deterministic functions\. The deterministic layer adds a median47​μ​s47\\,\\mu\\mathrm\{s\}atk=20k\{=\}20candidates \(single\-threaded Python 3\.13 on AMD Zen 3; Table[28](https://arxiv.org/html/2609.10413#A4.T28)\) with empirically linearO⁡\(k\)O\(k\)scaling, wherekkis the number of candidate edges scored after distillation\. Extended architecture details \(session initialization, per\-user parameter evolution, interpretability, safety\) are in Appendix[B](https://arxiv.org/html/2609.10413#A2)\.

### 3\.6FR\-Bank: Infrastructure\-Independent Implementation

To validate substrate independence we implement FR\-Bank, a standalone lifecycle bank replacing Graphiti with a flat embedding store, using one GPT\-4\.1\-mini call per turn for combined extraction and classification\. Retrieval merges cosine \(top\-60\), BM25 \(top\-20\) and category\-forced \(top\-20\) candidates, distills to top\-20, then applies the full lifecycle stack\. FR\-Bank needs no graph database, entity resolution, or deduplication, and all lifecycle parameters match the Graphiti configuration \(Appendix[Z](https://arxiv.org/html/2609.10413#A26)\)\.

## 4Theoretical Foundations

We use a generative model of active relevance \(Model 1\) to motivate FR’s feature set, then prove structural results establishing that the metadata basis\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)is necessary and sufficient for lifecycle\-aware scoring\. All proofs are in Appendix[A](https://arxiv.org/html/2609.10413#A1)\.

Notation\.At timett, letEtE\_\{t\}be the memory store\. Each edgee∈Ete\\in E\_\{t\}carries metadatam⁡\(e\)=\(ce,κe,ξe,he,te\)m\(e\)=\(c\_\{e\},\\kappa\_\{e\},\\xi\_\{e\},h\_\{e\},t\_\{e\}\), wherece∈𝒞c\_\{e\}\\in\\mathcal\{C\}is the behavioral category,κe\\kappa\_\{e\}is the normalized slot key,ξe∈\{active,superseded,expired,retracted\}\\xi\_\{e\}\\in\\\{\\texttt\{active\},\\texttt\{superseded\},\\texttt\{expired\},\\texttt\{retracted\}\\\}is lifecycle state,heh\_\{e\}is an optional event\-time anchor, andtet\_\{e\}is creation time\. WriteΔ​te=t−te\\Delta t\_\{e\}=t\-t\_\{e\}andσ⁡\(e,q\)∈\[0,1\]\\sigma\(e,q\)\\in\[0,1\]for semantic similarity to queryqq\. LetGeG\_\{e\}be the event thateesupports the answer,AeA\_\{e\}the event thateeis currently active for the query, andRkR\_\{k\}the retrieved set of sizekk\.

Model 1 \(Lifecycle active relevance\)\.For queryqqand candidate edgee∈Ete\\in E\_\{t\}, define

P\(Ge=1,Ae=1∣q,Et\)∝exp\{βσ\(e,q\)\}ρ\(ce∣q\)Sce\(Δte\)Vce\(t,he\)Ω\(e\)Mq\(ξe\),P\(G\_\{e\}=1,A\_\{e\}=1\\mid q,E\_\{t\}\)\\propto\\exp\\\{\\beta\\sigma\(e,q\)\\\}\\,\\rho\(c\_\{e\}\\mid q\)\\,S\_\{c\_\{e\}\}\(\\Delta t\_\{e\}\)\\,V\_\{c\_\{e\}\}\(t,h\_\{e\}\)\\,\\Omega\(e\)\\,M\_\{q\}\(\\xi\_\{e\}\),\(1\)whereρ⁡\(c∣q\)\\rho\(c\\mid q\)is a query\-category prior,Sc​\(d\)S\_\{c\}\(d\)is the category survival function with defaultSc​\(d\)=exp⁡\(−λc​d\)S\_\{c\}\(d\)=\\exp\(\-\\lambda\_\{c\}d\),Vc​\(t,h\)V\_\{c\}\(t,h\)is the event\-time validity kernel,Mq​\(ξe\)∈\{0,1\}M\_\{q\}\(\\xi\_\{e\}\)\\in\\\{0,1\\\}is a query\-conditioned compatibility mask on lifecycle state, andΩ\(e\)=∏e′:κe′=κe,te′\>te\(1−γe′→e\)\\Omega\(e\)=\\prod\_\{e^\{\\prime\}:\\,\\kappa\_\{e^\{\\prime\}\}=\\kappa\_\{e\},\\,t\_\{e^\{\\prime\}\}\>t\_\{e\}\}\(1\-\\gamma\_\{e^\{\\prime\}\\to e\}\)withγe′→e∈\[0,1\]\\gamma\_\{e^\{\\prime\}\\to e\}\\in\[0,1\]is the slot\-local supersession survival factor, taken over later edges sharingee’s slot key\.

Consequence 1 \(Plug\-in log\-score\)\.Under Model 1, taking logs yields the deterministic lifecycle score

ℓ⁡\(e,q,t\)=β​σ​\(e,q\)\+log⁡ρ⁡\(ce∣q\)−λce​Δ​te\+log⁡Vce​\(t,he\)\+log⁡Ω⁡\(e\)\+log⁡Mq​\(ξe\),\\ell\(e,q,t\)=\\beta\\sigma\(e,q\)\+\\log\\rho\(c\_\{e\}\\mid q\)\-\\lambda\_\{c\_\{e\}\}\\Delta t\_\{e\}\+\\log V\_\{c\_\{e\}\}\(t,h\_\{e\}\)\+\\log\\Omega\(e\)\+\\log M\_\{q\}\(\\xi\_\{e\}\),\(2\)with the conventionlog⁡0=−∞\\log 0=\-\\infty\. Model 1 is a modeling assumption, not a claim about runtime inference; FR computes deterministic policies over these quantities\. Its role is to expose the sufficient statistics of lifecycle\-aware active relevance: category controls survival and routing, slot key controls the competitor set used by supersession, lifecycle state gates query compatibility, and event\-time anchor controls future\- vs\. past\-oriented validity\.

Theorem 1 \(Lifecycle non\-identifiability\)\.Letsϕ​\(e,q\)=ϕ⁡\(σ⁡\(e,q\),Δ​te\)s\_\{\\phi\}\(e,q\)=\\phi\(\\sigma\(e,q\),\\Delta t\_\{e\}\)be any deterministic feature\-restricted scorer\. There exist two memory historiesHHandH′H^\{\\prime\}and a queryqqsuch that all candidates have identical\(σ,Δ​t\)\(\\sigma,\\Delta t\)profiles underHHandH′H^\{\\prime\}but the correct lifecycle\-aware rankings differ\. Consequentlysϕs\_\{\\phi\}produces the same ranking on both histories and fails on at least one; ifH,H′H,H^\{\\prime\}are a priori equiprobable, the binary error floor isPe≥1/2P\_\{e\}\\geq 1/2\.

*Proof sketch\.*The proof constructs two histories with identical\(σ,Δ​t\)\(\\sigma,\\Delta t\)profiles but different correct rankings due to hidden supersession structure \(Appendix[A\.2](https://arxiv.org/html/2609.10413#A1.SS2)\)\.

The missing quantity is not a better scalar weight but missing state: a flat retriever cannot recover slot\-local replacement, retraction, or future\-versus\-past event direction from\(σ,Δ​t\)\(\\sigma,\\Delta t\)because that information is absent from the representation\. Were this self\-evident, the dominant systems—Mem0, Memory\-R1, MemGPT, MemoryOS—would not all operate inside the regime it prohibits\.

Sufficiency, minimality, and individual necessity\.The metadata basis\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)is both sufficient \(Theorem 2\) and minimal \(Theorem 2′\): each component is individually necessary \(Theorem 3\), with explicit witnesses showing that removing category labels conflates preservation with suppression, removing slot keys conflates independent facts with competing ones, removing lifecycle state conflates current with historical queries, and removing event\-time anchors conflates upcoming with expired obligations\. Action\-space impossibility results \(Theorems 3′, 3′′in Appendices[A\.8](https://arxiv.org/html/2609.10413#A1.SS8)and[A\.9](https://arxiv.org/html/2609.10413#A1.SS9)\) further show that event\-time\-invariant and binary\-flat retraction\-oblivious systems have worst\-case error≥1/2\\geq 1/2\. Full statements and proofs are in Appendices[A\.3](https://arxiv.org/html/2609.10413#A1.SS3)–[A\.9](https://arxiv.org/html/2609.10413#A1.SS9)\.

Calibration as convex feasibility\.The feasible parameter regionΘm\\Theta\_\{m\}for lifecycle scoring is a convex polyhedron \(Theorem 4\)\. The global\-α\\alphafamily is a one\-dimensional slice ofΘm\\Theta\_\{m\}, and on our data that slice is empty:99\.8%99\.8\\%of the1,5661\{,\}566preservation–suppression cross\-pairs on FR\-Bank are jointly infeasible \(min⁡αFmax=1\.7×10−6\\min\\alpha\_\{F\}^\{\\max\}=1\.7\\times 10^\{\-6\}againstmax⁡αLmin≈1\.0\\max\\alpha\_\{L\}^\{\\min\}\\approx 1\.0\), and zero of the4545populated cells of the11×1111\\times 11category polytope admit a sharedα\\alpha\. Category\-specific blending parameters restore feasibility \(Appendix[A\.10](https://arxiv.org/html/2609.10413#A1.SS10)\)\. The rates are therefore hand\-set but*constraint\-derived*rather than fitted to benchmark outcomes, and behavior is insensitive inside the feasible region: ten of eleven categories tolerate the full0\.25×0\.25\\times–4×4\\timesmultiplier sweep at retrieval Jaccard≥0\.95\{\\geq\}\\,0\.95\(Table[36](https://arxiv.org/html/2609.10413#A9.T36)\), and a 20/20 persona holdout shows no overfitting \(77\.0%77\.0\\%vs\.76\.8%76\.8\\%, Fisherp=1\.00p=1\.00\)\.

Staleness has empirical bite\.Conditioning pass rate on context cleanliness givesPS​\(pass\)=\(1−πS\)​p0\+πS​p1P\_\{S\}\(\\textnormal\{pass\}\)=\(1\-\\pi\_\{S\}\)\\,p\_\{0\}\+\\pi\_\{S\}\\,p\_\{1\}withp0=75\.8%p\_\{0\}=75\.8\\%andp1=6\.0%p\_\{1\}=6\.0\\%empirically, so stale facts flip outcomes rather than acting as harmless noise; the contamination gap between FR\-Graphiti \(π=0\.08\\pi=0\.08\) and Mem0 \(π=0\.27\\pi=0\.27\) predicts a13\.313\.3pp pass advantage against an observed1212pp \(Appendix[A\.12](https://arxiv.org/html/2609.10413#A1.SS12)\)\.

Scope of these claims\.*Representation\-level impossibility*, holding for any scorer in the stated feature class regardless of training: Theorem 1, Theorem 3 with its four witnesses, and the action\-space analogs 3′and 3′′\.*Positive results about the basis*: Theorems 2 and 2′\.*Calibration feasibility*: Theorem 4\.*Empirical, contingent claims about deployed systems*: the staleness decomposition, Proposition 1, Proposition 3A \(falsified by our own data, Appendix[A\.12](https://arxiv.org/html/2609.10413#A1.SS12)\), and every cross\-system number in §[6](https://arxiv.org/html/2609.10413#S6)\. Two consequences follow\. The theory does*not*establish that the 10\+1 partition, the decay rates, or the pipeline are optimal; §[6\.7](https://arxiv.org/html/2609.10413#S6.SS7)measures how much the partition actually matters\. And a baseline carrying slot keys, event\-time anchors, retraction flags and query\-conditioned filters observes\(κ,h,ξ,Mq\)\(\\kappa,h,\\xi,M\_\{q\}\), so it falls*outside*the impossibility classes by construction—Theorems 2 and 2′say precisely that this basis suffices\. We build and measure that baseline in §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5), where what it loses turns out to be calibration rather than retrieval correctness, as Theorem 4 predicts\.

## 5LifecycleBench

LifecycleBench is a temporal disambiguation benchmark in which the correct answer depends on lifecycle state\. It comprises 516 questions over 40 synthetic personas, each with∼\{\\sim\}35 multi\-session conversations spanning 18 simulated months, structured into nine attack vectors \(Table[12](https://arxiv.org/html/2609.10413#A3.T12)\): superseded preference \(AV1,n=75n\{=\}75\), expired logistics \(AV2, 75\), stable identity buried under conversation volume \(AV3, 94\), multi\-version facts \(AV4, 44\), broad aggregation \(AV5, 40\), cross\-session contradiction \(AV6, 45\), selective forgetting after explicit retraction \(AV7, 40\), numeric preservation \(AV8, 63\), and soft supersession \(AV9, 40\)\. Personas span 14 nationalities and ages 22–68, generated conversation\-first under rules enforcing natural dialogue, with structured YAML ground truth enumerating supersession events, expiry dates, retraction language, and ambiguity\-resolution rules\. As in LongMemEval\[[1](https://arxiv.org/html/2609.10413#bib.bib1)\]and LoCoMo\[[13](https://arxiv.org/html/2609.10413#bib.bib13)\], conversations are synthetic because ground\-truth temporal state is unobservable without controlled design \(Appendix[C\.2](https://arxiv.org/html/2609.10413#A3.SS2)\)\. The attack vectors were defined from failure modes observed in preliminary evaluation of Mem0 and Zep/Graphiti, before FR’s mechanisms were designed, and all systems are evaluated under identical conditions\. FR does not dominate: MemoryOS leads AV6 \(73% vs\. 64%\) and AV7, FR\-Graphiti leads AV2 and AV8, and FR\-Bank scores only 5% retrieval pass on AV7; FR\-Bank leads AV1, AV3, AV4 and AV5 outright plus a three\-way AV9 tie, and Memory\-R1 leads none\. Because we introduce both benchmark and method, §[6\.6](https://arxiv.org/html/2609.10413#S6.SS6)reports a transfer to an externally constructed benchmark; Appendix[C\.6](https://arxiv.org/html/2609.10413#A3.SS6)analyzes co\-design risk directly, and Appendices[C\.3](https://arxiv.org/html/2609.10413#A3.SS3)and[C](https://arxiv.org/html/2609.10413#A3)give personas, the judge protocol, and extended methodology\.

## 6Experiments

Table[3](https://arxiv.org/html/2609.10413#S6.T3)consolidates results across LifecycleBench \(LCB\) and end\-to\-end response quality \(E2E\) for seven memory system configurations, with FR\-Graphiti ablation rows below the cross\-system comparison\.

Table 3:Consolidated results across LifecycleBench \(LCB\) and end\-to\-end response quality \(E2E\),n=516n=516; the rule separates cross\-system rows from FR\-Graphiti ablation rows\. Confabulation is reported under*both*denominators, with correct\-over\-total alongside so the abstention trade\-off is visible in the same row\. An abstention is never counted as a confabulation, and “all queries” means all 516 questions\.E2E, all queriesE2E, ans\.SystemLCB PassLCB StaleCorrectConfabConfabE2E SafeFR\-Bank76\.9%15\.5%31\.2%13\.0%22\.4%73\.3%FR\-Graphiti73%8%22\.9%13\.4%23\.9%66\.9%MemoryOS70\.5%7%13\.2%18\.4%40\.8%68\.0%Memory\-R166\.9%15\.3%19\.6%19\.4%31\.5%58\.2%A\-MEM65\.3%30\.4%18\.8%35\.1%47\.0%44\.2%Mem0 \(gpt\-4\.1\-mini\)67\.1%21\.5%27\.3%25\.4%33\.8%52\.1%Mem0 \(default\)61%27%18\.6%32\.2%45\.1%47\.3%FR\-Graphiti \(full\)73%8%––––−\-routing67%10%––––−\-behavioral decay66%16%––––baseline \(uniform, no rt\.\)61%18%––––Cross\-generator replication on Kimi K2\.5\[[23](https://arxiv.org/html/2609.10413#bib.bib23)\]preserves the confabulation rank order over the four core systems: FR\-Bank 26\.1% / 61\.0% safe vs\. Mem0 44\.4% / 40\.2% \(full breakdown including A\-MEM and Mem0\-mini, which show generator\-dependent shifts, in Appendix[AB](https://arxiv.org/html/2609.10413#A28)\)\.

### 6\.1LongMemEval\-S Under the Wu et al\. Protocol

FR\-Bank achieves75\.2%±0\.7075\.2\\%\\pm 0\.70pp pass@10 on the full 500\-question LongMemEval\-S benchmark\[[1](https://arxiv.org/html/2609.10413#bib.bib1)\]under the exact Wu et al\. \(ICLR 2025\) judge protocol \(Table[15](https://arxiv.org/html/2609.10413#A4.T15)\), to our knowledge the state of the art under the canonical rubric and above the closest peer\-reviewed result, RMM\[[3](https://arxiv.org/html/2609.10413#bib.bib3)\]at 70\.4% under a different judge configuration\. We hold the original five\-template rubric and judge model \(gpt\-4o\-2024\-08\-06\) fixed because subsequent work substitutes stronger answerers, different judges, and simplified prompts, rendering reported numbers mutually incomparable; methodology integrity rather than the absolute number is the point\. On the 317\-question matched subset the lifecycle layer is aggregate\-neutral \(\+2\.2\+2\.2pp net,72\.9%→75\.1%72\.9\\%\\to 75\.1\\%\), with a−6\.4\-6\.4pp effect on knowledge update \(79\.5%79\.5\\%vs\.85\.9%85\.9\\%\)\. We report that inversion as a benchmark\-criterion artifact rather than a lifecycle gain: the Wu et al\. judge credits a response when superseded facts appear alongside the updated answer, so filtering is penalized for cleaner context \(Appendix[D\.2](https://arxiv.org/html/2609.10413#A4.SS2)\)\. A\+6\.4\+6\.4pp knowledge\-update figure in the submitted version traced to no surviving artifact and is withdrawn \(Appendix[AI](https://arxiv.org/html/2609.10413#A35)\)\.

### 6\.2LifecycleBench Results

FR\-Bank attains76\.9%pass rate on LifecycleBench \(95% CI\[73\.3,80\.6\]\[73\.3,80\.6\]; Table[3](https://arxiv.org/html/2609.10413#S6.T3)\),\+16\+16pp over Mem0 and with1\.76×1\.76\\timeslower staleness\. The 4\-config ablation on FR\-Graphiti decomposes contributions: full lifecycle adds\+12\+12pp over the baseline \(uniform decay, no routing\); category\-aware routing alone contributes\+6\+6pp; behavioral decay contributes the remainder\. When the correct edge appears anywhere in the top\-10, 94\.5% of questions pass, confirming the bottleneck is retrieval recall rather than ranking\. Per\-attack\-vector breakdown \(largest gains:\+21\+21pp AV1 superseded preferences,\+20\+20pp AV2 expired logistics,\+22\+22pp AV4 multi\-version facts,\+10\+10pp AV7 selective forgetting\) and the full five\-system per\-AV comparison are in Appendix[D](https://arxiv.org/html/2609.10413#A4)\.

FR\-Bank’s 5% AV7 retrieval pass rate reflects intended behavior: retracted facts are correctly excluded from the retrieval set by the lifecycle state maskMq​\(ξ\)M\_\{q\}\(\\xi\)\. The low retrieval pass rate converts to the highest end\-to\-end correct rate among all evaluated systems \(37\.5%; Appendix[N](https://arxiv.org/html/2609.10413#A14)\) because the downstream model correctly abstains rather than confabulating over retracted plans\. Systems without retraction filtering achieve higher retrieval pass rates \(MemoryOS 57%\) but lower end\-to\-end correctness \(7\.5%\) because generic summaries pass retrieval evaluation by containing nothing specific to be wrong about\.

The full lifecycle stack contributes\+12\+12pp over the uniform baseline \(Table[3](https://arxiv.org/html/2609.10413#S6.T3)\)\. Replacing the behavioral partition with a cognitive \(Semantic/Episodic/Procedural\) one, holding the pipeline fixed, favors the behavioral partition on 7 of 9 attack vectors but by an aggregate margin of only1\.11\.1–1\.41\.4pp \(Table[4](https://arxiv.org/html/2609.10413#A1.T4), Appendix[A\.5](https://arxiv.org/html/2609.10413#A1.SS5)\); §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)explains why the margin is small—the choice of partition is not what carries retrieval correctness\. What category structure does carry is the ability to express per\-category parameters at all: without it there is no differential decay, no category\-specific blending, no routing, no feasible global blending weight \(Theorem 4\), and the stack falls back to the 61% uniform baseline\.

### 6\.3Cross\-System Comparison

All competitors run in shipped default configurations, matching the end\-user experience; versions, backbones, prompts, and known failure rates are in Appendices[O](https://arxiv.org/html/2609.10413#A15)and[P](https://arxiv.org/html/2609.10413#A16)\. Memory\-R1 uses GPT\-4\.1\-mini, well above its paper’s LLaMA\-3\.1\-8B, giving an upper bound on pre\-RL performance\. The AV2 and AV7 gaps are architectural, not capability\-dependent: event\-time expiry needs structural support absent from flat vector stores \(AV2: FR\-Bank 88% vs\. Mem0 65%\), and no prompting suppresses an explicitly retracted plan when retraction is not a primitive—on AV7 FR\-Bank reaches 37\.5% end\-to\-end correct, the highest of any system, while Memory\-R1 and Mem0 \(both 2\.5%\) confabulate over 90% downstream\. Memory\-R1’s learned \{ADD, UPDATE, DELETE\} space contains no expiry or retraction action; these are vocabulary gaps, not optimization failures\. Substrate independence holds across two implementations of the same policies \(Graphiti 73%, flat bank 76\.9%\)\. A\-MEM\[[4](https://arxiv.org/html/2609.10413#bib.bib4)\]pairs the highest retrieval recall \(87\.6% Hit@5\) with the highest staleness \(30\.4%\) and worst confabulation \(47\.0%\), so recall without lifecycle management actively hurts downstream; upgrading Mem0’s extractor to gpt\-4\.1\-mini raises pass rate to 67\.1% \(\+6\.1\+6\.1pp\) but leaves AV2 and AV7 unchanged \(Appendix[O](https://arxiv.org/html/2609.10413#A15)\)\.

### 6\.4End\-to\-End Response Quality

For each of 516 LifecycleBench questions, each system’s top\-10 retrieved facts are provided as the sole context to GPT\-5\.4 \(temperature 0, max\_tokens=500\) with a system prompt restricting answers to the provided facts; an independent Claude Sonnet judge then classifies each response as correct, partial, wrong, or abstain and flags confabulation \(full methodology in Appendix[N](https://arxiv.org/html/2609.10413#A14)\)\. The resulting confabulation hierarchy maps directly to architectural staleness management: over answered queries, FR\-Bank \(22\.4%\)<<FR\-Graphiti \(23\.9%\)<<Memory\-R1 \(31\.5%\)<<Mem0\-mini \(33\.8%\)<<MemoryOS \(40\.8%\)<<Mem0 \(45\.1%\)<<A\-MEM \(47\.0%\)\. Because a system that abstains more shows a lower rate under that denominator regardless of its behavior on answered questions, we report every rate over all 516 queries as well \(Table[3](https://arxiv.org/html/2609.10413#S6.T3), Appendix[AF](https://arxiv.org/html/2609.10413#A32)\)\. The gap survives essentially intact—19\.219\.2of the22\.722\.7pp FR\-Bank – Mem0 gap remains \(13\.0%13\.0\\%vs\.32\.2%32\.2\\%\)—and correct\-over\-total moves the same way \(31\.2%31\.2\\%vs\.18\.6%18\.6\\%\), so the extra abstentions are not bought with correct answers\. The ranking is stable under both denominators; the one movement is MemoryOS, whose low all\-queries confabulation \(18\.4%18\.4\\%\) pairs the highest abstain rate \(54\.8%54\.8\\%\) with the lowest correct rate \(13\.2%13\.2\\%\), an instance of the retrieval\-metric paradox below\. Cross\-generator replication on Kimi K2\.5 preserves the four\-system core ranking with a∼\\sim15pp tier gap between lifecycle\-managed and unmanaged systems on both generators, evidence against GPT\-family training artifacts \(Appendix[AB](https://arxiv.org/html/2609.10413#A28)\)\.

Safe response rate\.FR\-Bank’s higher abstain rate \(42\.1% vs\. Mem0’s 28\.7%; FR\-Graphiti abstains at 44\.0%\) reflects deliberate safety: lifecycle filtering removes stale facts, leaving the model with insufficient context, and the model correctly declines rather than confabulating\. The safe response rate \(correct\+\+abstain\) captures this: FR\-Bank at 73\.3% vs\. Mem0 at 47\.3%\.

Reasoning partially mitigates contamination \(−4\.5\-4\.5pp on Mem0’s context with GPT\-5\.4 reasoning enabled\) but leaves an18\.218\.2pp architectural gap no downstream compute closes\. A retrieval\-metric paradox also appears: MemoryOS reaches70\.5%70\.5\\%retrieval pass but only13\.2%13\.2\\%E2E correct, because hierarchical summarization substitutes generic summaries that pass retrieval evaluation by containing nothing specific to be wrong about\. On AV7 this becomes an inversion, and it is a direct instance of Proposition 3A’s falsified invariance \(Appendix[A\.12](https://arxiv.org/html/2609.10413#A1.SS12)\): were retrieval pass a monotone predictor of end\-to\-end correctness, MemoryOS \(57%57\\%AV7 retrieval pass\) would beat FR\-Bank \(5%5\\%\), yet FR\-Bank scores37\.5%37\.5\\%correct against MemoryOS’s7\.5%7\.5\\%\. Retrieval pass measures context cleanliness and is blind to informativeness, so wherever correct behavior is*absence*rather than*presence*the two decouple and retrieval\-level evaluation becomes adversely informative\.

### 6\.5Attribution: What the Ontology Contributes

Comparisons against external systems cannot separate FR’s two layers: the generic lifecycle metadata \(slot keys, event\-time anchors, retraction states\) and the behavioral typing above it\. We therefore ran a within\-pipeline ablation under a design pre\-registered before data contact\. The untyped arm keeps three deterministic primitives—slot\-key supersession, event\-time expiry, retraction masking—and removes everything typed, ranking by*semantic similarity alone*over an unmasked cosine\+\+BM25 pool with no routing, category\-forced retrieval, or multi\-hop expansion\. Being more austere than a single\-variable ablation, it lower\-bounds a lifecycle\-metadata\-only system rather than isolating the category labels exactly \(Appendix[AD](https://arxiv.org/html/2609.10413#A30)\)\.

On correctness the arms are statistically indistinguishable\(Δ=−1\.7\\Delta=\-1\.7pp, 95% CI\[−6\.0,\+2\.7\]\[\-6\.0,\+2\.7\], McNemarp=0\.44p=0\.44\): the generic metadata, not the behavioral ontology, carries FR’s correctness advantage, and the abstract states the claim that way\.What the typed layer carries is calibration\.All\-queries confabulation falls from24\.2%24\.2\\%\(125/516125/516\) under the untyped arm to12\.0%12\.0\\%\(62/51662/516\) under the full stack \(Δ=−12\.2\\Delta=\-12\.2pp, 95% CI\[−16\.1,−8\.2\]\[\-16\.1,\-8\.2\],p<0\.001p<0\.001\), with 84 questions confabulated only by the untyped arm against 21 only by the full stack; abstention rises15\.915\.9pp while correct\-over\-total is unchanged, so the extra abstentions come from would\-be wrong answers rather than correct ones\. This is the failure mode the theory names: the necessity witness for the category labelcc\(Appendix[A\.7\.1](https://arxiv.org/html/2609.10413#A1.SS7.SSS1)\) is a cross\-intent*scoring*conflict—theα\\alpha\-feasibility conflict of Theorem 4—not a retrieval failure\. Both arms were scored in one paired pass over byte\-identical FR\-Bank answers; under the original pass FR\-Bank’s all\-queries confabulation reads13\.0%13\.0\\%rather than12\.0%12\.0\\%, a five\-question difference within judge noise that leaves every contrast above unaffected \(Appendix[AD](https://arxiv.org/html/2609.10413#A30)\)\.

How fine must the partition be?Merging the eleven policy cells by policy similarity and sweepingk=1,3,5,7,9,11k=1,3,5,7,9,11end\-to\-end on BEAM, with every mechanism on so only granularity varies, gives118,120,125,133,130,131118,120,125,\\mathbf\{133\},130,131correct of 280, with contradiction resolution rising monotonically \(19,22,22,27,27,2919,22,22,27,27,29\) and knowledge update flat at everykk\. Granularity is load\-bearing \(k=1→k=7k\{=\}1\\to k\{=\}7:\+15\+15correct,\+5\.4\+5\.4pp\) and then saturates: the peak isk=7k\{=\}7, andk=7,9,11k=7,9,11span three questions, within noise\. This reproduces the paper’s own variance analysis, where the optimal 8\-partition already attains the 11\-partition variance floor \(Table[5](https://arxiv.org/html/2609.10413#A1.T5)\)\. We therefore keep 10\+1 for interpretability—human\-readable per\-domain labels for user\-facing memory control—rather than claiming granularity\-11 is uniquely necessary\.

### 6\.6External Transfer: BEAM

Because we introduce both the benchmark and the method, the decisive test of co\-design is an external one\. We evaluated on BEAM\[[14](https://arxiv.org/html/2609.10413#bib.bib14)\]: 100 coherent conversations and 2,000 human\-validated questions across ten memory abilities, constructed independently of this work, three of whose abilities \(contradiction resolution, event ordering, instruction following\) were newly introduced by its authors and therefore cannot derive from FR’s design or from the failure modes that informed LifecycleBench\. The FR\-vs\-Mem0 comparison and the restriction to the five lifecycle\-relevant abilities at the 1M\-token tier were pre\-registered before data contact; all arms share one harness and one frozen judge\. That judge over\-abstains relative to the frozen API judge used elsewhere in this paper, so on BEAM confabulation counts are lower bounds and abstention rates upper bounds—uniformly across arms, leaving between\-arm comparisons unaffected \(Appendix[AE](https://arxiv.org/html/2609.10413#A31)\)\.

Over the four binary\-scorable abilities \(n=70n=70each\), reported as FR\-full \(k=11k\{=\}11\) / FR with the ontology collapsed to a single global\-mean cell \(k=1k\{=\}1, every lifecycle mechanism retained\) / Mem0: contradiction resolution𝟐𝟗/19/5\\mathbf\{29\}/19/5, temporal reasoning𝟐𝟔/24/15\\mathbf\{26\}/24/15, knowledge update33/𝟑𝟒/𝟑𝟒33/\\mathbf\{34\}/\\mathbf\{34\}, abstention𝟒𝟑/41/38\\mathbf\{43\}/41/38\. In total, FR\-full is correct on𝟏𝟑𝟏\\mathbf\{131\}of280280\(46\.8%46\.8\\%\) against118118\(42\.1%42\.1\\%\) fork=1k\{=\}1and9292\(32\.9%32\.9\\%\) for Mem0, with confabulation𝟕𝟐\\mathbf\{72\}/8484/108108\.

The lifecycle advantage transfers, and decomposes as it does on LifecycleBench: the untyped configuration already beats Mem0, and the typed layer adds a further gain concentrated in contradiction resolution \(2929vs\.1919of7070; McNemar exactp≈0\.006p\\approx 0\.006\)\. Re\-executed identically, FR\-full spans125125–131131of280280across three runs, so the decomposition is reported as*ranges*:\+23\+23to\+26\+26correct from the generic metadata and\+10\+10to\+13\+13from the ontology\. Two independently specified minimal arms—thek=1k\{=\}1collapse above, and a separate arm using untyped defaults that scores115/280115/280overall—both land on exactly19/7019/70contradiction resolution, so an untyped stack’s contradiction deficit replicates across operationalizations\. Knowledge update is a three\-way tie, as the theory predicts: plain updates need only slot\-key supersession, which Mem0’s UPDATE already provides, so there is no structural gap there to find\. Event ordering needs BEAM’s graded native metric; rescored under BEAM’s official scorer after a disclosed audit of our judge’s ordering handling, FR leads Mem0 on both \(τnorm\\tau\_\{\\text\{norm\}\}0\.2140\.214vs\.0\.1900\.190, Wilcoxonp=0\.009p=0\.009;llm\_judge0\.5740\.574vs\.0\.5100\.510,p=0\.020p=0\.020\) while the two FR arms are indistinguishable, and it is excluded from the binary aggregate\.

What does not replicate, and what it costs\.Three negatives ship with this result rather than after it, in full in Appendix[AE](https://arxiv.org/html/2609.10413#A31)\. The*correctness*half of the decomposition replicates; the*confabulation*half does not \(108→84→72108\\to 84\\to 72primary,108→76→75108\\to 76\\to 75on re\-execution\), so on BEAM we credit the confabulation reduction to the generic metadata alone\. A*lifecycle\-off*configuration of the same stack scores135/280135/280, above both typed arms, on knowledge update4343vs\.3333:1010of the1212discordant cases trace to ingest\-time supersession firing under over\-broad slot keys and deactivating the entry carrying the current value—the slot\-key fragility §[6\.7](https://arxiv.org/html/2609.10413#S6.SS7)identifies—and the untyped arm inherits it \(knowledge update3131\), so the cost sits in the generic primitives, not the ontology\. We state that trade rather than netting it out\. And no arm orders events at all in absolute terms: exact\-correct is0/700/70for all three, so theτnorm\\tau\_\{\\text\{norm\}\}separation sits on a floor of zero\.

### 6\.7Robustness and Validation of Our Own Judge

The deterministic layer consumes LLM\-generated metadata, so its robustness is bounded by that metadata’s quality\. Injecting independent noise per field at ingestion, recomputing lifecycle states, and rerunning retrieval localizes the exposure sharply \(Appendix[AH](https://arxiv.org/html/2609.10413#A34)\): at 10% corruption Jaccard@10 falls to0\.7640\.764/0\.8370\.837under slot\-key merge/split corruption but only to0\.9170\.917under category\-label flips and0\.9930\.993/0\.9990\.999under anchor deletion and±7\\pm 7\-day shifts\. Sensitivity concentrates on the field §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)identifies as carrying correctness, while the field carrying calibration is tolerant—even a 50% category flip costs\+2\.7\+2\.7pp of staleness\. Retraction is the most potent field per corrupted edge and the least prevalent \(31 of18,93618\{,\}936edges\), and its binding constraint is extraction*recall*: the detector fires on 19 of 40 scripted retractions and only 2 of 40 are cleanly suppressed at the metadata level, so FR\-Bank’s37\.5%37\.5\\%AV7 correctness is recovered downstream—the generator reconciling a co\-retrieved plan and its cancellation—rather than by clean exclusion\. The classifier itself is audited atκ=\+0\.67\\kappa=\+0\.67\(n=188n=188\), disagreements falling on pairs whose policies are nearly identical and therefore least consequential \(Appendix[B\.1\.1](https://arxiv.org/html/2609.10413#A2.SS1.SSS1)\)\.

Our end\-to\-end judge is itself an LLM, so we audited it the same way with two machine instruments \(Appendix[AG](https://arxiv.org/html/2609.10413#A33)\)\. A six\-model cross\-family panel agrees with itself \(Fleissκ=0\.834\\kappa=0\.834\) more than with our pinned judge \(κ=0\.715\\kappa=0\.715\) and localizes the discrepancy: the pinned judge over\-appliespartialto answers that are incomplete but uncontaminated\. Re\-judging all748748partialverdicts plus a 60\-item control under an independent judge lifts correct and safe rates55–77pp roughly uniformly, leaves the ranking unchanged on every metric, moves the FR\-Bank – Mem0 correct gap from\+12\.6\+12\.6to\+11\.0\+11\.0pp, and reproduces93%93\\%of controls; three of our four pre\-registered predictions were refuted\. Absolute rates are therefore judge\-relative, and the cross\-system comparisons are the robust findings\.

## 7Discussion and Conclusion

Limitations\.Five, in the order we consider them binding\. \(i\)*Human validation is absent\.*Every verdict here comes from an LLM judge; we audited it with two machine instruments \(§[6\.7](https://arxiv.org/html/2609.10413#S6.SS7)\) that agree on the direction of its bias but not its magnitude, and the classifier is audited against LLM judges rather than humans\. A stratified human\-labeled slice \(100 verdicts, two non\-author annotators blind to system identity, prioritizing items where the machine judges disagree\) is planned and*has not yet been run*; until it is, absolute rates are judge\-relative\. \(ii\)*Benchmark–method co\-design risk\.*We built LifecycleBench, and its attack vectors were informed by failure modes we observed in baselines\. The BEAM transfer bounds this risk without eliminating it, and BEAM’s runs use a different backbone, so they are not commensurable with our LifecycleBench tables\. \(iii\)*Comparison fairness\.*Competitors run in shipped defaults against a deliberately engineered FR stack\. The untyped\-arm decomposition separates policy from engineering within our own stack and Appendix[E](https://arxiv.org/html/2609.10413#A5)documents each external system’s structural blocker, but a maximally tuned competitor was not built\. \(iv\)*No multi\-framework or multi\-agent evaluation\.*FR is presented as composable yet tested on two substrates and one agent loop; behavior under other frameworks or concurrent writers is unmeasured\. \(v\)*The correctness–abstention trade\-off is real\.*FR\-Bank answers57\.9%57\.9\\%of queries; §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)shows the extra abstentions come from would\-be wrong answers, but a deployment that must always answer will not benefit as reported\.

Further scope notes: rate calibration is constraint\-driven rather than metric\-optimized, with a 20/20 persona holdout confirming generalization \(77\.0%77\.0\\%vs\.76\.8%76\.8\\%, Fisherp=1\.00p=1\.00\); the seven configurations span five architectural paradigms; and soft supersession fails under high\-commitment generators \(Kimi AV9\), where leaving both candidate values in the set produces commitment rather than abstention\. Extended discussion is in Appendix[AC](https://arxiv.org/html/2609.10413#A29); every number changed relative to the submitted version is in Appendix[AI](https://arxiv.org/html/2609.10413#A35)\.

Privacy, consent, and safety\.Memory systems that retain personal facts raise privacy and safety concerns beyond those addressed in this work, including consent, verifiable deletion, prompt\-injection defenses, and cultural generalization of decay assumptions; we discuss these in Appendix[AC\.1](https://arxiv.org/html/2609.10413#A29.SS1)\.

Conclusion\.Fortunate Recall attaches lifecycle metadata to every stored fact and applies deterministic, category\-conditioned policies over it\. Two implementations of the same stack achieve indistinguishable LifecycleBench pass rates \(p=0\.10p=0\.10\) while cutting downstream confabulation from Mem0’s45\.1%45\.1\\%to22\.4%22\.4\\%over answered queries and from32\.2%32\.2\\%to13\.0%13\.0\\%over all queries, answering more questions correctly in the process, and non\-identifiability and individual\-necessity theorems establish the basis\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)as structurally necessary\. Our controlled ablation then divides the credit within that basis, and we state the division as the paper’s claim: the*generic*metadata carries the correctness advantage, while the*behavioral ontology*makes per\-category calibration feasible where no global weight is, halves confabulation, and adds one localized, replicated correctness gain on contradiction resolution, its granularity benefit saturating near seven policy clusters\. That claim is narrower than the one we submitted, and it transfers to a benchmark we did not build\.

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## Supplementary Materials

## Appendix AProofs and Theoretical Details

### A\.1Model 1 and Its Deterministic Consequence

We restate Model 1 for convenience:

P\(Ge=1,Ae=1∣q,Et\)∝exp\{βσ\(e,q\)\}ρ\(ce∣q\)Sce\(Δte\)Vce\(t,he\)Ω\(e\)Mq\(ξe\)\.P\(G\_\{e\}=1,A\_\{e\}=1\\mid q,E\_\{t\}\)\\propto\\exp\\\{\\beta\\sigma\(e,q\)\\\}\\,\\rho\(c\_\{e\}\\mid q\)\\,S\_\{c\_\{e\}\}\(\\Delta t\_\{e\}\)\\,V\_\{c\_\{e\}\}\(t,h\_\{e\}\)\\,\\Omega\(e\)\\,M\_\{q\}\(\\xi\_\{e\}\)\.\(3\)HereMq​\(ξe\)M\_\{q\}\(\\xi\_\{e\}\)is a deterministic compatibility mask: for a current\-state query it is11onactiveand00otherwise; for a historical query it may also admitsuperseded; for a deletion\-sensitive query it excludesretracted; and so on\. The exact intent\-to\-mask map is a policy choice, but the existence of such a query\-conditioned mask is the relevant structural fact\.

With the exponential survival functionSc​\(d\)=exp⁡\(−λc​d\)S\_\{c\}\(d\)=\\exp\(\-\\lambda\_\{c\}d\), taking logs of \([3](https://arxiv.org/html/2609.10413#A1.E3)\) yields

ℓ⁡\(e,q,t\)=β​σ​\(e,q\)\+log⁡ρ⁡\(ce∣q\)−λce​Δ​te\+log⁡Vce​\(t,he\)\+log⁡Ω⁡\(e\)\+log⁡Mq​\(ξe\),\\ell\(e,q,t\)=\\beta\\sigma\(e,q\)\+\\log\\rho\(c\_\{e\}\\mid q\)\-\\lambda\_\{c\_\{e\}\}\\Delta t\_\{e\}\+\\log V\_\{c\_\{e\}\}\(t,h\_\{e\}\)\+\\log\\Omega\(e\)\+\\log M\_\{q\}\(\\xi\_\{e\}\),\(4\)with the conventionlog⁡0=−∞\\log 0=\-\\infty\. This is the deterministic plug\-in score used only as an interpretation device\. FR itself evaluates deterministic lifecycle rules rather than posterior probabilities\.

### A\.2Proof of Theorem 1

#### A\.2\.1Exact non\-identifiability

Theorem 1 \(restated\)\.For any deterministic feature\-restricted scorersϕ​\(e,q\)=ϕ⁡\(σ⁡\(e,q\),Δ​te\)s\_\{\\phi\}\(e,q\)=\\phi\(\\sigma\(e,q\),\\Delta t\_\{e\}\), there exist two historiesHHandH′H^\{\\prime\}with identical observed\(σ,Δ​t\)\(\\sigma,\\Delta t\)profiles but different correct rankings\.

###### Proof\.

Consider two candidate edgeseoe\_\{o\}andene\_\{n\}and a common queryqq\. Let

\(σ⁡\(eo,q\),Δ​to\)=\(0\.96,30\),\(σ⁡\(en,q\),Δ​tn\)=\(0\.94,1\)\.\(\\sigma\(e\_\{o\},q\),\\Delta t\_\{o\}\)=\(0\.96,30\),\\qquad\(\\sigma\(e\_\{n\},q\),\\Delta t\_\{n\}\)=\(0\.94,1\)\.\(5\)Thus every feature\-restricted scorer computes the same two numbers in every history:sϕ​\(eo,q\)=ϕ⁡\(0\.96,30\)s\_\{\\phi\}\(e\_\{o\},q\)=\\phi\(0\.96,30\)andsϕ​\(en,q\)=ϕ⁡\(0\.94,1\)s\_\{\\phi\}\(e\_\{n\},q\)=\\phi\(0\.94,1\)\.

Now define two histories\.

*HistoryHH\.*The later edge supersedes the earlier one:κeo=κen\\kappa\_\{e\_\{o\}\}=\\kappa\_\{e\_\{n\}\}andγen→eo=1\\gamma\_\{e\_\{n\}\\to e\_\{o\}\}=1\. For a current\-state query, the correct lifecycle\-aware ranking is

en≻eo\.e\_\{n\}\\succ e\_\{o\}\.\(6\)
*HistoryH′H^\{\\prime\}\.*The two edges do not compete:κeo≠κen\\kappa\_\{e\_\{o\}\}\\neq\\kappa\_\{e\_\{n\}\}\(or equivalently the update confidence is00\)\. Both edges remain active, and becauseeoe\_\{o\}is the more semantically aligned fact, the correct ranking is

eo≻en\.e\_\{o\}\\succ e\_\{n\}\.\(7\)
The observed pairs in \([5](https://arxiv.org/html/2609.10413#A1.E5)\) are identical underHHandH′H^\{\\prime\}, sosϕs\_\{\\phi\}must output the same ranking on both histories\. But \([6](https://arxiv.org/html/2609.10413#A1.E6)\) and \([7](https://arxiv.org/html/2609.10413#A1.E7)\) differ\. Thereforesϕs\_\{\\phi\}fails on at least one of the two histories\. IfHHandH′H^\{\\prime\}are equiprobable, any decision rule based only on the common output ofsϕs\_\{\\phi\}has error probability at least1/21/2\. ∎

#### A\.2\.2Deterministicε\\varepsilon\-relaxation

We now weaken strict intent\-opacity to bounded opacity\.

Assumption A\.1 \(Lipschitz scorer\)\.There existsL\>0L\>0such that

\|ϕ⁡\(σ,Δ​t\)−ϕ⁡\(σ′,Δ​t\)\|≤L​\|σ−σ′\|∀σ,σ′∈\[0,1\],∀Δ​t≥0\.\\big\|\\phi\(\\sigma,\\Delta t\)\-\\phi\(\\sigma^\{\\prime\},\\Delta t\)\\big\|\\leq L\\,\|\\sigma\-\\sigma^\{\\prime\}\|\\qquad\\forall\\sigma,\\sigma^\{\\prime\}\\in\[0,1\],\\ \\forall\\Delta t\\geq 0\.\(8\)
Fix a reference intenti0i\_\{0\}and writesi​\(j\)=ϕ⁡\(σ⁡\(ej,qi\),Δ​tj\)s\_\{i\}\(j\)=\\phi\(\\sigma\(e\_\{j\},q\_\{i\}\),\\Delta t\_\{j\}\),s¯​\(j\)=si0​\(j\)\\bar\{s\}\(j\)=s\_\{i\_\{0\}\}\(j\)\. Lete\(1\),…,e\(m\)e\_\{\(1\)\},\\ldots,e\_\{\(m\)\}be the candidates ordered by the reference scoress¯​\(e\(1\)\)≥⋯≥s¯​\(e\(m\)\)\\bar\{s\}\(e\_\{\(1\)\}\)\\geq\\cdots\\geq\\bar\{s\}\(e\_\{\(m\)\}\)\. Define the minimum adjacent margin

Δmin=minr=1,…,m−1⁡\[s¯​\(e\(r\)\)−s¯​\(e\(r\+1\)\)\]\.\\Delta\_\{\\min\}=\\min\_\{r=1,\\ldots,m\-1\}\\left\[\\bar\{s\}\(e\_\{\(r\)\}\)\-\\bar\{s\}\(e\_\{\(r\+1\)\}\)\\right\]\.\(9\)
Theorem A\.1 \(Lipschitz refinement of Theorem 1\)\.If the query ensemble isε\\varepsilon\-intent\-opaque and2​L​ε<Δmin2L\\varepsilon<\\Delta\_\{\\min\}, then the induced rankingπ^ϕ\\hat\{\\pi\}\_\{\\phi\}is identical for all intents in the ensemble, henceI⁡\(Intent,π^ϕ\)=0I\(\\mathrm\{Intent\};\\hat\{\\pi\}\_\{\\phi\}\)=0\.

###### Proof\.

For any edgeeje\_\{j\}and intentsi,i′i,i^\{\\prime\},

\|si​\(j\)−si′​\(j\)\|=\|ϕ⁡\(σ⁡\(ej,qi\),Δ​tj\)−ϕ⁡\(σ⁡\(ej,qi′\),Δ​tj\)\|≤L\|σ⁡\(ej,qi\)−σ⁡\(ej,qi′\)\|≤L​ε,\|s\_\{i\}\(j\)\-s\_\{i^\{\\prime\}\}\(j\)\|=\\left\|\\phi\(\\sigma\(e\_\{j\},q\_\{i\}\),\\Delta t\_\{j\}\)\-\\phi\(\\sigma\(e\_\{j\},q\_\{i^\{\\prime\}\}\),\\Delta t\_\{j\}\)\\right\|\\leq L\\,\|\\sigma\(e\_\{j\},q\_\{i\}\)\-\\sigma\(e\_\{j\},q\_\{i^\{\\prime\}\}\)\|\\leq L\\varepsilon,\(10\)using Lipschitz continuity andε\\varepsilon\-intent\-opacity\. Hence for any pairj,kj,k,

\|\(si​\(j\)−si​\(k\)\)−\(si′​\(j\)−si′​\(k\)\)\|≤\|si​\(j\)−si′​\(j\)\|\+\|si​\(k\)−si′​\(k\)\|≤2​L​ε\.\\big\|\(s\_\{i\}\(j\)\-s\_\{i\}\(k\)\)\-\(s\_\{i^\{\\prime\}\}\(j\)\-s\_\{i^\{\\prime\}\}\(k\)\)\\big\|\\leq\|s\_\{i\}\(j\)\-s\_\{i^\{\\prime\}\}\(j\)\|\+\|s\_\{i\}\(k\)\-s\_\{i^\{\\prime\}\}\(k\)\|\\leq 2L\\varepsilon\.\(11\)
Now fix any adjacent pair\(e\(r\),e\(r\+1\)\)\(e\_\{\(r\)\},e\_\{\(r\+1\)\}\)in the reference ranking\. Its baseline gap is at leastΔmin\\Delta\_\{\\min\}by definition\. If2​L​ε<Δmin2L\\varepsilon<\\Delta\_\{\\min\}, then \([11](https://arxiv.org/html/2609.10413#A1.E11)\) implies that the sign of every adjacent score difference is preserved for every intent:si​\(e\(r\)\)−si​\(e\(r\+1\)\)\>0s\_\{i\}\(e\_\{\(r\)\}\)\-s\_\{i\}\(e\_\{\(r\+1\)\}\)\>0for alliiandrr\. Therefore all adjacent relations are unchanged, so the full ranking is unchanged\. Sinceπ^ϕ\\hat\{\\pi\}\_\{\\phi\}is constant as a function of intent,I⁡\(Intent,π^ϕ\)=H⁡\(π^ϕ\)−H⁡\(π^ϕ∣Intent\)=0I\(\\mathrm\{Intent\};\\hat\{\\pi\}\_\{\\phi\}\)=H\(\\hat\{\\pi\}\_\{\\phi\}\)\-H\(\\hat\{\\pi\}\_\{\\phi\}\\mid\\mathrm\{Intent\}\)=0\. ∎

##### Operational consequence\.

When semantic differences between temporal intents are much smaller than the score margin required to change the ranking, intent information is exactly absent from the output of any feature\-restricted scorer\.

#### A\.2\.3A looser stochastic entropy bound

The deterministic bound above is the clean result\. Some reviewers nevertheless prefer a “soft” information\-theoretic expression rather than a hard margin criterion\. To obtain that, an additional stochastic assumption is necessary\.

Assumption A\.2 \(Comparison\-flip model\)\.For each unordered pair\(j,k\)\(j,k\)with1≤j<k≤m1\\leq j<k\\leq m, define the Bernoulli variable

Bj​k=\{the relative order of​ej​and​ek​differs from the reference ranking under the realized intent\}\.B\_\{jk\}=\\mathbf\{1\}\\\!\\left\\\{\\text\{the relative order of \}e\_\{j\}\\text\{ and \}e\_\{k\}\\text\{ differs from the reference ranking under the realized intent\}\\right\\\}\.Assume that

P⁡\(Bj​k=1\)≤p∀1≤j<k≤m,P\(B\_\{jk\}=1\)\\leq p\\qquad\\forall\\,1\\leq j<k\\leq m,\(12\)for somep≤min⁡\{12,2​L​ε/Δmin\}p\\leq\\min\\\!\\left\\\{\\frac\{1\}\{2\},2L\\varepsilon/\\Delta\_\{\\min\}\\right\\\}\.

##### Important scope note\.

The entropy bound below is*not*a consequence ofε\\varepsilon\-intent\-opacity alone\. It additionally assumes the comparison\-flip model of Assumption A\.2\. The exact and fully rigorous deterministic statement remains Theorem A\.1; Proposition A\.1 is a weaker corollary that trades a sharper deterministic conclusion for a softer information\-theoretic framing\.

Proposition A\.1 \(Entropy bound under Assumption A\.2\)\.Under Assumption A\.2,

I⁡\(Intent,π^ϕ\)≤\(m2\)​h2​\(p\)≤\(m2\)​h2​\(min⁡\{12,2​L​εΔmin\}\)\.I\(\\mathrm\{Intent\};\\hat\{\\pi\}\_\{\\phi\}\)\\leq\\binom\{m\}\{2\}h\_\{2\}\(p\)\\leq\\binom\{m\}\{2\}h\_\{2\}\\\!\\left\(\\min\\\!\\left\\\{\\frac\{1\}\{2\},\\frac\{2L\\varepsilon\}\{\\Delta\_\{\\min\}\}\\right\\\}\\right\)\.\(13\)
###### Proof\.

The rankingπ^ϕ\\hat\{\\pi\}\_\{\\phi\}is a deterministic function of the full pairwise comparison patternB=\{Bj​k:1≤j<k≤m\}B=\\\{B\_\{jk\}:1\\leq j<k\\leq m\\\}, because a total order is determined by the relative order of every pair of items\. Therefore, by the data processing inequality,

I⁡\(Intent,π^ϕ\)≤I⁡\(Intent,B\)\.I\(\\mathrm\{Intent\};\\hat\{\\pi\}\_\{\\phi\}\)\\leq I\(\\mathrm\{Intent\};B\)\.\(14\)By the chain rule and the fact that conditioning cannot increase entropy,

I⁡\(Intent,B\)≤H⁡\(B\)≤∑1≤j<k≤mH⁡\(Bj​k\)\.I\(\\mathrm\{Intent\};B\)\\leq H\(B\)\\leq\\sum\_\{1\\leq j<k\\leq m\}H\(B\_\{jk\}\)\.\(15\)EachBj​kB\_\{jk\}is Bernoulli with parameter at mostpp\. Sinceh2h\_\{2\}is monotone increasing on\[0,1/2\]\[0,1/2\],H⁡\(Bj​k\)≤h2​\(min⁡\{p,1/2\}\)H\(B\_\{jk\}\)\\leq h\_\{2\}\(\\min\\\{p,1/2\\\}\)\. There are\(m2\)\\binom\{m\}\{2\}unordered pairs, soI⁡\(Intent,π^ϕ\)≤\(m2\)​h2​\(p\)I\(\\mathrm\{Intent\};\\hat\{\\pi\}\_\{\\phi\}\)\\leq\\binom\{m\}\{2\}h\_\{2\}\(p\)\. The second inequality in \([13](https://arxiv.org/html/2609.10413#A1.E13)\) follows from the assumed bound onpp\. ∎

#### A\.2\.4Measured values, two regimes, and the binary case

##### Measuredε\\varepsilonand activation gaps\.

Direct measurement across 73 current/superseded edge pairs on LifecycleBench \(embedding modeltext\-embedding\-3\-small,dim=1536\\dim=1536\) yields

median​\|ε\|=0\.060,median​\|Δ​a\|≈3\.3×10−10,median​αrequired=0\.9998\.\\mathrm\{median\}\\,\|\\varepsilon\|=0\.060,\\qquad\\mathrm\{median\}\\,\|\\Delta a\|\\approx 3\.3\\times 10^\{\-10\},\\qquad\\mathrm\{median\}\\,\\alpha\_\{\\mathrm\{required\}\}=0\.9998\.\(16\)

##### Two regimes\.

*Short\-term regime \(Δ​t<500\\Delta t<500hr\):*activation differences are meaningful, so the margin condition2​L​ε<Δmin2L\\varepsilon<\\Delta\_\{\\min\}can hold\. Plugging in an illustrativeΔmin=0\.30\\Delta\_\{\\min\}=0\.30withL=1L=1and the measuredε=0\.060\\varepsilon=0\.060gives2​L​ε=0\.12<0\.302L\\varepsilon=0\.12<0\.30; Theorem A\.1 applies and

I⁡\(Intent,π^ϕ\)=0I\(\\mathrm\{Intent\};\\hat\{\\pi\}\_\{\\phi\}\)=0\(17\)within the ensemble\. If the two intents are equiprobable and require different correct rankings, any estimator based onπ^ϕ\\hat\{\\pi\}\_\{\\phi\}has error probability

Pe≥12\.P\_\{e\}\\geq\\tfrac\{1\}\{2\}\.\(18\)*Long\-term regime \(Δ​t\>2000\\Delta t\>2000hr\):*activations underflow to≈0\\approx 0for all competing edges—empirically3\.3×10−103\.3\\times 10^\{\-10\}at the median—so the blended score collapses to pure semantic similarity, which carries medianε=0\.060\\varepsilon=0\.060between current and superseded facts\. The requiredα≈1\\alpha\\approx 1cannot be satisfied while simultaneously preserving numeric facts, so the scalar family is feasibility\-empty in this regime\. FR bypasses the regime via supersession filtering, event\-time expiry, and category\-forced retrieval\.

##### Fano\-style entropy bound \(short\-term regime\)\.

Applying the looser stochastic bound withm=2m=2in the short\-term regime,p≤2​L​ε/Δmin=0\.12/0\.30=0\.4p\\leq 2L\\varepsilon/\\Delta\_\{\\min\}=0\.12/0\.30=0\.4, so

I⁡\(Intent,π^ϕ\)≤h2​\(0\.4\)≈0\.971​bits\.I\(\\mathrm\{Intent\};\\hat\{\\pi\}\_\{\\phi\}\)\\leq h\_\{2\}\(0\.4\)\\approx 0\.971\\text\{ bits\}\.\(19\)For binary intents, classical Fano in the formPe≥\(H⁡\(X∣Y\)−1\)/log2⁡KP\_\{e\}\\geq\(H\(X\\mid Y\)\-1\)/\\log\_\{2\}Kis vacuous becauseK=2K=2makes the numerator nonpositive\. The correct binary relation is

H⁡\(X∣Y\)≤h2​\(Pe\)\.H\(X\\mid Y\)\\leq h\_\{2\}\(P\_\{e\}\)\.\(20\)SinceH⁡\(X\)=1H\(X\)=1bit andI⁡\(X,Y\)≤0\.971I\(X;Y\)\\leq 0\.971, one hasH⁡\(X∣Y\)≥0\.029H\(X\\mid Y\)\\geq 0\.029\. Using the monotonicity ofh2h\_\{2\}on\[0,1/2\]\[0,1/2\],

Pe≥h2−1​\(0\.029\)≈0\.003\.P\_\{e\}\\geq h\_\{2\}^\{\-1\}\(0\.029\)\\approx 0\.003\.\(21\)The stochastic bound is much weaker than the exact50%50\\%floor from \([18](https://arxiv.org/html/2609.10413#A1.E18)\), confirming that the deterministic margin argument is the right operational statement\. In the long\-term regime the deterministic argument already forcesPe≥1/2P\_\{e\}\\geq 1/2with no stochastic assumption\.

### A\.3Proof of Theorem 2

Theorem 2\.Under Model 1, lifecycle\-aware scoring can be computed from\(σ⁡\(e,q\),ce,κe,ξe,he,Δ​te\)\\big\(\\sigma\(e,q\),c\_\{e\},\\kappa\_\{e\},\\xi\_\{e\},h\_\{e\},\\Delta t\_\{e\}\\big\)given the memory storeEtE\_\{t\}and the deterministic policy maps\.

###### Proof\.

Start from the plug\-in score \([4](https://arxiv.org/html/2609.10413#A1.E4)\)\. Each term is determined as follows:

1. 1\.β​σ​\(e,q\)\\beta\\sigma\(e,q\)depends only onσ⁡\(e,q\)\\sigma\(e,q\)\.
2. 2\.log⁡ρ⁡\(ce∣q\)\\log\\rho\(c\_\{e\}\\mid q\)depends on the category labelcec\_\{e\}and the query\.
3. 3\.−λce​Δ​te\-\\lambda\_\{c\_\{e\}\}\\Delta t\_\{e\}depends oncec\_\{e\}andΔ​te\\Delta t\_\{e\}\.
4. 4\.log⁡Vce​\(t,he\)\\log V\_\{c\_\{e\}\}\(t,h\_\{e\}\)depends oncec\_\{e\},tt, andheh\_\{e\}\.
5. 5\.log⁡Ω⁡\(e\)\\log\\Omega\(e\)depends on the set of later edges with the same slot keyκe\\kappa\_\{e\}and their supersession confidences, so it is determined byκe\\kappa\_\{e\}together with the history\.
6. 6\.log⁡Mq​\(ξe\)\\log M\_\{q\}\(\\xi\_\{e\}\)depends only on the lifecycle stateξe\\xi\_\{e\}and the query\-conditioned compatibility map\.

Therefore any two candidate edges that agree on\(σ⁡\(e,q\),ce,κe,ξe,he,Δ​te\)\\big\(\\sigma\(e,q\),c\_\{e\},\\kappa\_\{e\},\\xi\_\{e\},h\_\{e\},\\Delta t\_\{e\}\\big\)receive the same score\. Hence that tuple, together with the storeEtE\_\{t\}\(which determinesΩ⁡\(e\)\\Omega\(e\)via the slot\-local supersession history\), is sufficient for lifecycle\-aware scoring under Model 1\. ∎

##### Equivalent encodings\.

The theorem does not preclude alternative encodings\. If another representation stores exactly the same information under a different parameterization, it is equally sufficient\.

### A\.4Proof of Minimality \(Theorem 2′\)

The submitted version stated this result in prose; we give the formal statement here, as requested during review\.

###### Theorem 2′\(Minimality of the metadata basis\)\.

LetB=\{c,κ,ξ,h\}B=\\\{c,\\kappa,\\xi,h\\\}be the metadata basis and letB′⊊BB^\{\\prime\}\\subsetneq Bbe any strict subset\. Then there exists a lifecycle taskT⁡\(B′\)T\(B^\{\\prime\}\)—a distribution over memory histories and queries—on which every deterministic scorer measurable with respect to\(σ,Δ​t,B′\)\\bigl\(\\sigma,\\Delta t,B^\{\\prime\}\\bigr\)attains error at least1/21/2, while some deterministic scorer measurable with respect to\(σ,Δ​t,B\)\(\\sigma,\\Delta t,B\)attains error00\. ConsequentlyBBis minimal: no proper subset of it is sufficient in the sense of Theorem 2\.

We strengthen Theorem 2 from sufficiency to minimality: every strict subset of\{c,κ,ξ,h\}\\\{c,\\kappa,\\xi,h\\\}, even augmented with\(σ,Δ​t\)\(\\sigma,\\Delta t\), admits a lifecycle task on which deterministic scorers err at rate at least1/21/2\.

##### Indistinguishable\-pair lemma\.

LetI0,I1I^\{0\},I^\{1\}be two lifecycle instances satisfying

Φℱ​\(I0\)=Φℱ​\(I1\),y⁡\(I0\)≠y⁡\(I1\),\\Phi\_\{\\mathcal\{F\}\}\(I^\{0\}\)=\\Phi\_\{\\mathcal\{F\}\}\(I^\{1\}\),\\qquad y\(I^\{0\}\)\\neq y\(I^\{1\}\),\(22\)whereΦℱ\\Phi\_\{\\mathcal\{F\}\}is the projection to\(σ,Δ​t\)\(\\sigma,\\Delta t\)together with the variables inℱ\\mathcal\{F\}, andyyis the correct binary pairwise label\. Under the uniform distribution over\{I0,I1\}\\\{I^\{0\},I^\{1\}\\\}, every deterministic scorer over\(σ,Δ​t\)×ℱ\(\\sigma,\\Delta t\)\\times\\mathcal\{F\}with deterministic tie\-breaking has error probability at least1/21/2\.

###### Proof\.

Deterministic scoring and tie\-breaking make the scorer’s decisiona∈\{0,1\}a\\in\\\{0,1\\\}a function ofΦℱ\\Phi\_\{\\mathcal\{F\}\}alone\. By \([22](https://arxiv.org/html/2609.10413#A1.E22)\),aais identical onI0I^\{0\}andI1I^\{1\}, but the labels differ\. Exactly one of the two equally weighted instances is misclassified, soPe=1/2P\_\{e\}=1/2\. ∎

##### Witness verification\.

We verify that each Appendix[A\.7](https://arxiv.org/html/2609.10413#A1.SS7)witness satisfies the stronger requirement of the lemma: fixing the removed variable, the three*other*metadata variables are identical across the two histories\.

- •*Category*\([A\.7\.1](https://arxiv.org/html/2609.10413#A1.SS7.SSS1), Eq\. \([31](https://arxiv.org/html/2609.10413#A1.E31)\)\): both instances fixκ=κ0\\kappa=\\kappa\_\{0\},ξ=active\\xi=\\texttt\{active\},h=∅h=\\varnothing; onlyccdiffers \(Financial vs Logistical\)\.
- •*Slot key*\([A\.7\.2](https://arxiv.org/html/2609.10413#A1.SS7.SSS2), Eq\. \([34](https://arxiv.org/html/2609.10413#A1.E34)\)\): both histories sharec=Prefc=\\texttt\{Pref\},ξ=active\\xi=\\texttt\{active\},h=∅h=\\varnothing, and identical\(σ,Δ​t\)\(\\sigma,\\Delta t\); onlyκ\\kappadiffers\.
- •*Lifecycle state*\([A\.7\.3](https://arxiv.org/html/2609.10413#A1.SS7.SSS3), Eq\. \([37](https://arxiv.org/html/2609.10413#A1.E37)\)\): both edges sharec=Prefc=\\texttt\{Pref\},κ=food\_pref\\kappa=\\texttt\{food\\\_pref\},h=∅h=\\varnothing, and the two query intents produce opposite labels on the same\(σ,Δ​t,c,κ,h\)\(\\sigma,\\Delta t,c,\\kappa,h\)tuple\.
- •*Event\-time*\([A\.7\.4](https://arxiv.org/html/2609.10413#A1.SS7.SSS4), Eqs\. \([40](https://arxiv.org/html/2609.10413#A1.E40)\)–\([41](https://arxiv.org/html/2609.10413#A1.E41)\)\): both obligation edges sharec=Oblc=\\texttt\{Obl\},κ=dentist\\kappa=\\texttt\{dentist\},ξ=active\\xi=\\texttt\{active\}, and identical\(σ,Δ​t\)\(\\sigma,\\Delta t\); onlyhhdiffers \(upcoming vs expired\)\.

##### Minimality\.

Letℱ⊊\{c,κ,ξ,h\}\\mathcal\{F\}\\subsetneq\\\{c,\\kappa,\\xi,h\\\}and pick anyx∈\{c,κ,ξ,h\}∖ℱx\\in\\\{c,\\kappa,\\xi,h\\\}\\setminus\\mathcal\{F\}\. Use the witnessTxT\_\{x\}forxx\. The witness makes all of\{c,κ,ξ,h\}∖\{x\}\\\{c,\\kappa,\\xi,h\\\}\\setminus\\\{x\\\}identical across the two instances, andℱ⊆\{c,κ,ξ,h\}∖\{x\}\\mathcal\{F\}\\subseteq\\\{c,\\kappa,\\xi,h\\\}\\setminus\\\{x\\\}, soΦℱ​\(I0\)=Φℱ​\(I1\)\\Phi\_\{\\mathcal\{F\}\}\(I^\{0\}\)=\\Phi\_\{\\mathcal\{F\}\}\(I^\{1\}\)\. The labels differ\. By the lemma,Pe≥1/2P\_\{e\}\\geq 1/2\. ∎

### A\.5The Behavioral Ontology as an Empirical Variance\-Minimizing Partition

Table 4:Ontology ablation on LifecycleBench, referenced from §[6](https://arxiv.org/html/2609.10413#S6)\. Same FR\-Bank pipeline, same stored edges, same judge; only the category\-to\-parameter mapping changes\. Cognitive categories: Semantic \(Identity, Relational, Intellectual, Health, Financial\), Episodic \(Obligations, Logistical\), Procedural \(Preferences, Hobbies, Projects\)\. The behavioral partition wins 7 of 9 attack vectors under arithmetic aggregation and 4 of 5 non\-tied vectors under harmonic\. The77\.5%77\.5\\%cell is a distinct ontology\-ablation run; its0\.60\.6pp difference from the canonical76\.9%76\.9\\%of Table[3](https://arxiv.org/html/2609.10413#S6.T3)is judge non\-determinism across separate runs, well inside the observed variance \(Table[15](https://arxiv.org/html/2609.10413#A4.T15)\) and the canonical 95% CI\[73\.3,80\.6\]\[73\.3,80\.6\]\.ConfigurationPass RateStalenessWins/9 AVsBehavioral \(10\+1 categories\)77\.5%16\.1%—Cognitive \(3 cat\., arith\.λ\\lambda\)76\.4%16\.7%2Cognitive \(3 cat\., harm\.λ\\lambda\)76\.2%17\.1%1The behavioral\-versus\-cognitive contrast in Table[4](https://arxiv.org/html/2609.10413#A1.T4)should be read alongside §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)and §[6\.7](https://arxiv.org/html/2609.10413#S6.SS7): the aggregate margin between partitions is small because the partition is not what carries retrieval correctness, and the cognitive 3\-partition is in any case a particularly poor 3\-partition rather than a representative one—it merges the two categories with maximally divergent lifecycle policies \(Obligations, floor0\.700\.70; Logistical Context, floor0\.000\.00\) into a single Episodic cell\. The exhaustive enumeration below shows the*optimal*3\-partition achieving substantially lower within\-cell policy variance than the cognitive one, so the small delta in Table[4](https://arxiv.org/html/2609.10413#A1.T4)reflects the cognitive partition’s accidental rate calibration rather than the unimportance of partition structure\.

The old circular proposition “if category labels determine lifecycle policy, then lifecycle policy can be computed from category labels” is not a theorem\. The correct, testable statement is an empirical partition\-quality claim\.

Letπ^​\(e\)∈ℝd\\hat\{\\pi\}\(e\)\\in\\mathbb\{R\}^\{d\}be an estimated per\-edge policy vector\. In practice one can takeπ^​\(e\)=\(λ^e,α^e,F^e,u^e,v^e\)\\hat\{\\pi\}\(e\)=\(\\hat\{\\lambda\}\_\{e\},\\hat\{\\alpha\}\_\{e\},\\hat\{F\}\_\{e\},\\hat\{u\}\_\{e\},\\hat\{v\}\_\{e\}\), where the coordinates are fit from oracle lifecycle decisions or from the minimal parameter values needed to satisfy the benchmark constraints for that edge\.

For a candidate categorizationCC, define the sample within\-category policy variance

V^\(C\)=∑c∈im⁡\(C\)ncn1nc−1∑e:C⁡\(e\)=c∥π^\(e\)−π¯c∥22,π¯c=1nc∑e:C⁡\(e\)=cπ^\(e\)\.\\widehat\{V\}\(C\)=\\sum\_\{c\\in\\mathrm\{im\}\(C\)\}\\frac\{n\_\{c\}\}\{n\}\\,\\frac\{1\}\{n\_\{c\}\-1\}\\sum\_\{e:\\,C\(e\)=c\}\\\|\\hat\{\\pi\}\(e\)\-\\bar\{\\pi\}\_\{c\}\\\|\_\{2\}^\{2\},\\qquad\\bar\{\\pi\}\_\{c\}=\\frac\{1\}\{n\_\{c\}\}\\sum\_\{e:\\,C\(e\)=c\}\\hat\{\\pi\}\(e\)\.\(23\)
Proposition 1 \(empirical\)\.The FR behavioral ontology is designed to minimizeV^​\(C\)\\widehat\{V\}\(C\)relative to coarser alternatives:

V^​\(Cbehavioral\)<V^​\(Ccognitive\)<V^​\(Cuniform\)\.\\widehat\{V\}\(C\_\{\\mathrm\{behavioral\}\}\)<\\widehat\{V\}\(C\_\{\\mathrm\{cognitive\}\}\)<\\widehat\{V\}\(C\_\{\\mathrm\{uniform\}\}\)\.\(24\)
##### Why this is not circular\.

Equation \([24](https://arxiv.org/html/2609.10413#A1.E24)\) is a statement about measured residual variance under competing partitions\. It could be false\. It is therefore falsifiable and empirical, rather than definitional\.

##### Measurement protocol\.

To test \([24](https://arxiv.org/html/2609.10413#A1.E24)\): \(i\) inferπ^​\(e\)\\hat\{\\pi\}\(e\)for each edge from oracle retrieval constraints or edge\-local calibration; \(ii\) assign each edge to categories under the three competing schemes; \(iii\) computeV^​\(C\)\\widehat\{V\}\(C\)using \([23](https://arxiv.org/html/2609.10413#A1.E23)\); \(iv\) compare the resulting variances\.

##### Empirical validation\.

We execute the measurement protocol above on the full FR\-Bank corpus \(12,968 active entries across 40 persona banks\), computingπ^​\(e\)=\(λ^e,α^e,F^e\)\\hat\{\\pi\}\(e\)=\(\\hat\{\\lambda\}\_\{e\},\\hat\{\\alpha\}\_\{e\},\\hat\{F\}\_\{e\}\)as the arithmetic weighted mean of per\-category policy vectors\(λc,αc,floorc\)\(\\lambda\_\{c\},\\alpha\_\{c\},\\mathrm\{floor\}\_\{c\}\)under each entry’s soft category membership weights:

V^​\(Cbehavioral\)=3\.60×10−3,V^​\(Ccognitive\)=2\.09×10−2,V^​\(Cuniform\)=4\.69×10−2\.\\widehat\{V\}\(C\_\{\\mathrm\{behavioral\}\}\)=3\.60\\times 10^\{\-3\},\\quad\\widehat\{V\}\(C\_\{\\mathrm\{cognitive\}\}\)=2\.09\\times 10^\{\-2\},\\quad\\widehat\{V\}\(C\_\{\\mathrm\{uniform\}\}\)=4\.69\\times 10^\{\-2\}\.\(25\)The strict orderingV^​\(Cbehavioral\)<V^​\(Ccognitive\)<V^​\(Cuniform\)\\widehat\{V\}\(C\_\{\\mathrm\{behavioral\}\}\)<\\widehat\{V\}\(C\_\{\\mathrm\{cognitive\}\}\)<\\widehat\{V\}\(C\_\{\\mathrm\{uniform\}\}\)holds, confirming Proposition 1\. The relative gap\(V^​\(Ccognitive\)−V^​\(Cbehavioral\)\)/V^​\(Cuniform\)=36\.9%\\bigl\(\\widehat\{V\}\(C\_\{\\mathrm\{cognitive\}\}\)\-\\widehat\{V\}\(C\_\{\\mathrm\{behavioral\}\}\)\\bigr\)/\\widehat\{V\}\(C\_\{\\mathrm\{uniform\}\}\)=36\.9\\%\(bootstrap95%95\\%CI:\[36\.0%,37\.6%\]\[36\.0\\%,\\ 37\.6\\%\],10001000resamples, seed=42=42\), exceeding the analytical lower bound of10\.1%10\.1\\%from the category\-mean model \(§[A\.6](https://arxiv.org/html/2609.10413#A1.SS6)\) by3\.6×3\.6\\times\. The behavioral partition reduces within\-cluster variance to7\.7%7\.7\\%of the uniform baseline; the cognitive partition only reduces it to44\.6%44\.6\\%\.

Per\-cognitive\-cell decomposition identifies the Episodic cell as the variance hot\-spot: merging Obligations \(floor=0\.70\\mathrm\{floor\}=0\.70\) and Logistical Context \(floor=0\.00\\mathrm\{floor\}=0\.00\) into a single “Episodic” cell produces within\-cell floor variance of7\.84×10−27\.84\\times 10^\{\-2\}, which dominates the cognitive partition’s total excess\. This is the cleanest evidence that the cognitive typology is policy\-incoherent: categories with maximally divergent lifecycle policies are merged because they share the same cognitive form \(time\-bound events\)\.

##### Granularity sweep\.

To test whether the 10\+1 ontology sits at a natural granularity sweet spot, we computeV^​\(𝒞\)\\widehat\{V\}\(\\mathcal\{C\}\)for partitions atK=1K=1\(uniform\) throughK=11K=11\(full behavioral\)\. At eachKKwe report both a user\-specified partition \(chosen by domain intuition\) and the*optimal*KK\-partition—the partition of 11 categories intoKKgroups that minimizesV^\\widehat\{V\}, found by exhaustive enumeration over the sufficient statistics\.

Table 5:Ontology granularity sweep\.V^user\\widehat\{V\}\_\{\\text\{user\}\}is the intuitive partition at eachKK;V^opt\\widehat\{V\}\_\{\\text\{opt\}\}is the minimum\-varianceKK\-partition\. The behavioralK=11K\{=\}11partition matches the optimal floor exactly\. The cognitiveK=3K\{=\}3partition is4\.2×4\.2\\timesworse than the optimalK=3K\{=\}3\.KKV^user\\widehat\{V\}\_\{\\text\{user\}\}V^opt\\widehat\{V\}\_\{\\text\{opt\}\}V^/V^uni\\widehat\{V\}/\\widehat\{V\}\_\{\\text\{uni\}\}\(user / opt\)1 \(uniform\)4\.68×10−24\.68\\times 10^\{\-2\}4\.68×10−24\.68\\times 10^\{\-2\}100%100\\%3 \(cognitive\)2\.09×10−22\.09\\times 10^\{\-2\}4\.99×10−34\.99\\times 10^\{\-3\}44\.5%44\.5\\%/10\.7%10\.7\\%5 \(semantic split\)2\.10×10−22\.10\\times 10^\{\-2\}3\.84×10−33\.84\\times 10^\{\-3\}44\.7%44\.7\\%/8\.2%8\.2\\%8 \(optimal only\)—3\.61×10−33\.61\\times 10^\{\-3\}— /7\.7%7\.7\\%11 \(behavioral\)3\.60×10−33\.60\\times 10^\{\-3\}3\.60×10−33\.60\\times 10^\{\-3\}7\.7%7\.7\\%Two findings emerge\. First, the full behavioral partition \(K=11K\{=\}11\) achieves the optimal floor: no rearrangement of categories into 11 groups produces lower within\-cluster variance, confirming the partition is not arbitrary\. Second, the cognitive partition’s failure is structural, not a granularity artifact: even the*optimal*K=3K\{=\}3partition \(V^=4\.99×10−3\\widehat\{V\}=4\.99\\times 10^\{\-3\},10\.7%10\.7\\%of uniform\) is4\.2×4\.2\\timesbetter than the cognitiveK=3K\{=\}3\(V^=2\.09×10−2\\widehat\{V\}=2\.09\\times 10^\{\-2\},44\.5%44\.5\\%\)\. The cognitive typology does not merely use too few categories—it merges the*wrong*categories, grouping Obligations \(floor=0\.70\{\}=0\.70\) with Logistical Context \(floor=0\.00\{\}=0\.00\) into a single “Episodic” cell despite maximally divergent lifecycle policies\.

##### Available evidence\.

The held\-out classifier audit reports70\.7%70\.7\\%majority\-vote agreement \(κ=\+0\.673\\kappa=\+0\.673,n=188n=188; Table[8](https://arxiv.org/html/2609.10413#A2.T8)\); errors concentrate on category pairs that share similar lifecycle policies and therefore have minimal downstream impact \(Appendix[B\.1\.1](https://arxiv.org/html/2609.10413#A2.SS1.SSS1.Px1)\)\. The full\-vs\-uniform ablation \(73%73\\%vs61%61\\%pass\) and the large gains on AV1/AV2/AV4/AV7 indicate that the behavioral partition separates facts precisely where lifecycle\-policy variance is largest\. These results are consistent with \([24](https://arxiv.org/html/2609.10413#A1.E24)\), though we present it as an empirical design claim rather than an analytic theorem\.

### A\.6Partition Separation: The Behavioral Variance Gap

###### Theorem 2A \(Partition variance gap\)\.

We prove the weighted pairwise identity underlying Theorem 2A and plug in the numerical bound from the FR ontology\.

##### The identity\.

LetGjG\_\{j\}be a cognitive cell with behavioral categories of weightwc=ncw\_\{c\}=n\_\{c\}and total weightWj=∑c∈GjwcW\_\{j\}=\\sum\_\{c\\in G\_\{j\}\}w\_\{c\}, and letθ¯j=Wj−1​∑c∈Gjwc​θc\\bar\{\\theta\}\_\{j\}=W\_\{j\}^\{\-1\}\\sum\_\{c\\in G\_\{j\}\}w\_\{c\}\\theta\_\{c\}\. Then

∑c∈Gjwc​‖θc−θ¯j‖2=1Wj​∑c1<c2c1,c2∈Gjwc1​wc2​‖θc1−θc2‖2\.\\sum\_\{c\\in G\_\{j\}\}w\_\{c\}\\\|\\theta\_\{c\}\-\\bar\{\\theta\}\_\{j\}\\\|^\{2\}=\\frac\{1\}\{W\_\{j\}\}\\sum\_\{\\begin\{subarray\}\{c\}c\_\{1\}<c\_\{2\}\\\\ c\_\{1\},c\_\{2\}\\in G\_\{j\}\\end\{subarray\}\}w\_\{c\_\{1\}\}w\_\{c\_\{2\}\}\\\|\\theta\_\{c\_\{1\}\}\-\\theta\_\{c\_\{2\}\}\\\|^\{2\}\.\(26\)
###### Proof\.

Expanding the LHS:∑cwc​‖θc−θ¯j‖2=∑cwc​‖θc‖2−Wj​‖θ¯j‖2=∑cwc​‖θc‖2−Wj−1​‖∑cwc​θc‖2\\sum\_\{c\}w\_\{c\}\\\|\\theta\_\{c\}\-\\bar\{\\theta\}\_\{j\}\\\|^\{2\}=\\sum\_\{c\}w\_\{c\}\\\|\\theta\_\{c\}\\\|^\{2\}\-W\_\{j\}\\\|\\bar\{\\theta\}\_\{j\}\\\|^\{2\}=\\sum\_\{c\}w\_\{c\}\\\|\\theta\_\{c\}\\\|^\{2\}\-W\_\{j\}^\{\-1\}\\big\\\|\\sum\_\{c\}w\_\{c\}\\theta\_\{c\}\\big\\\|^\{2\}\. Expanding the RHS using‖θc1−θc2‖2=‖θc1‖2\+‖θc2‖2−2​⟨θc1,θc2⟩\\\|\\theta\_\{c\_\{1\}\}\-\\theta\_\{c\_\{2\}\}\\\|^\{2\}=\\\|\\theta\_\{c\_\{1\}\}\\\|^\{2\}\+\\\|\\theta\_\{c\_\{2\}\}\\\|^\{2\}\-2\\langle\\theta\_\{c\_\{1\}\},\\theta\_\{c\_\{2\}\}\\rangleand collecting:Wj−1​∑c1<c2wc1​wc2​‖θc1−θc2‖2=∑cwc​‖θc‖2−Wj−1​‖∑cwc​θc‖2W\_\{j\}^\{\-1\}\\sum\_\{c\_\{1\}<c\_\{2\}\}w\_\{c\_\{1\}\}w\_\{c\_\{2\}\}\\\|\\theta\_\{c\_\{1\}\}\-\\theta\_\{c\_\{2\}\}\\\|^\{2\}=\\sum\_\{c\}w\_\{c\}\\\|\\theta\_\{c\}\\\|^\{2\}\-W\_\{j\}^\{\-1\}\\big\\\|\\sum\_\{c\}w\_\{c\}\\theta\_\{c\}\\big\\\|^\{2\}\. The two sides agree\. ∎

##### Class\-averaged gap\.

Dividing \([26](https://arxiv.org/html/2609.10413#A1.E26)\) bynjn\_\{j\}and averaging over theK′K^\{\\prime\}cognitive cells gives

V⁡\(𝒞cog\)−V⁡\(𝒞beh\)=1K′​∑j=1K′∑c1<c2c1,c2∈Gjnc1​nc2nj2​‖θc1−θc2‖2,V\(\\mathcal\{C\}\_\{\\mathrm\{cog\}\}\)\-V\(\\mathcal\{C\}\_\{\\mathrm\{beh\}\}\)=\\frac\{1\}\{K^\{\\prime\}\}\\sum\_\{j=1\}^\{K^\{\\prime\}\}\\sum\_\{\\begin\{subarray\}\{c\}c\_\{1\}<c\_\{2\}\\\\ c\_\{1\},c\_\{2\}\\in G\_\{j\}\\end\{subarray\}\}\\frac\{n\_\{c\_\{1\}\}\\,n\_\{c\_\{2\}\}\}\{n\_\{j\}^\{2\}\}\\,\\\|\\theta\_\{c\_\{1\}\}\-\\theta\_\{c\_\{2\}\}\\\|^\{2\},\(27\)under the category\-mean modelπ∗​\(e\)=θc⁡\(e\)\+εe\\pi^\{\*\}\(e\)=\\theta\_\{c\(e\)\}\+\\varepsilon\_\{e\}with𝔼⁡\[εe∣c\]=0\\mathbb\{E\}\[\\varepsilon\_\{e\}\\mid c\]=0: theεe\\varepsilon\_\{e\}contribution is a noise floor that is identical under every partition, and the between\-category terms‖θc1−θc2‖2\\\|\\theta\_\{c\_\{1\}\}\-\\theta\_\{c\_\{2\}\}\\\|^\{2\}that the cognitive partition merges are the extra variance a coarsening must absorb\.

##### Numerical plug\-in\.

Using the ten categories with clean\(λc,αc\)\(\\lambda\_\{c\},\\alpha\_\{c\}\)from Tables[48](https://arxiv.org/html/2609.10413#A21.T48)and[49](https://arxiv.org/html/2609.10413#A22.T49)and the cognitive partition

Semantic=\{Identity, Relational, Intellectual, Health, Financial\},\\displaystyle=\\\{\\text\{Identity, Relational, Intellectual, Health, Financial\}\\\},Episodic=\{Obligations, Logistical\},\\displaystyle=\\\{\\text\{Obligations, Logistical\}\\\},Procedural=\{Preferences, Hobbies, Projects\},\\displaystyle=\\\{\\text\{Preferences, Hobbies, Projects\}\\\},withnc=1n\_\{c\}=1for every category, the within\-cell variances are

WSem=0\.00100,WEpi=0\.000626,WPro=0\.00222,W\_\{\\text\{Sem\}\}=0\.00100,\\qquad W\_\{\\text\{Epi\}\}=0\.000626,\\qquad W\_\{\\text\{Pro\}\}=0\.00222,\(28\)yielding a class\-averaged gap

V⁡\(𝒞cog\)−V⁡\(𝒞beh\)≥13​\(0\.00100\+0\.000626\+0\.00222\)≈0\.00128\.V\(\\mathcal\{C\}\_\{\\mathrm\{cog\}\}\)\-V\(\\mathcal\{C\}\_\{\\mathrm\{beh\}\}\)\\geq\\tfrac\{1\}\{3\}\\big\(0\.00100\+0\.000626\+0\.00222\\big\)\\approx 0\.00128\.\(29\)The pooled 10\-category variance isV⁡\(𝒞uniform\)=0\.01273V\(\\mathcal\{C\}\_\{\\mathrm\{uniform\}\}\)=0\.01273, so the relative gap is

V⁡\(𝒞cog\)−V⁡\(𝒞beh\)V⁡\(𝒞uniform\)≥0\.001280\.01273≈10\.1%\.\\frac\{V\(\\mathcal\{C\}\_\{\\mathrm\{cog\}\}\)\-V\(\\mathcal\{C\}\_\{\\mathrm\{beh\}\}\)\}\{V\(\\mathcal\{C\}\_\{\\mathrm\{uniform\}\}\)\}\\geq\\frac\{0\.00128\}\{0\.01273\}\\approx 10\.1\\%\.\(30\)

##### α\\alpha\-dominance is structural\.

The pooled variance decomposes into0\.012730\.01273fromαc\\alpha\_\{c\}and4\.4×10−64\.4\\times 10^\{\-6\}fromλc\\lambda\_\{c\}: the gap is dominated by the blending coordinate\.αc\\alpha\_\{c\}governs the trade\-off between category\-conditional activation and raw semantic similarity—it is the category\-specific coordinate through which the ontology*enters*the lifecycle policy\. Partition separation is therefore a measurement of architecturally meaningful variance, not of a free hyperparameter\.

##### Remark onV⁡\(𝒞beh\)V\(\\mathcal\{C\}\_\{\\mathrm\{beh\}\}\)\.

Under the one\-θ\\theta\-per\-category model used here,V⁡\(𝒞beh\)=0V\(\\mathcal\{C\}\_\{\\mathrm\{beh\}\}\)=0exactly\. With real edge distributions,V⁡\(𝒞beh\)V\(\\mathcal\{C\}\_\{\\mathrm\{beh\}\}\)is the noise floor𝔼​‖εe‖2\\mathbb\{E\}\\\|\\varepsilon\_\{e\}\\\|^\{2\}, identical under every partition; the inequality in \([27](https://arxiv.org/html/2609.10413#A1.E27)\) is unchanged because the noise cancels\.

##### Empirical confirmation\.

The empirical measurement on the full corpus \(§[A\.5](https://arxiv.org/html/2609.10413#A1.SS5)\) confirms and substantially exceeds this bound: the measured relative gap is36\.9%36\.9\\%versus the analytical lower bound of10\.1%10\.1\\%, with the difference attributable to soft membership weights amplifying cross\-category spread beyond what the one\-θ\\theta\-per\-category model captures\.

##### Lifecycle and ontology are not independent\.

The lifecycle stack contributes\+\+12pp over the uniform baseline; the behavioral ontology contributes a further 1\.16–1\.36pp of calibration precision\. The two are not independent: the ontology is the interpretation layer through which lifecycle mechanisms receive their per\-category parameters\. The\+\+12pp gain requires*some*category structure; the behavioral partition fine\-tunes that structure to its empirically optimal configuration\. The ontology is to lifecycle policy what hyperparameter tuning is to model architecture—it does not create the capability, but it determines whether the capability is correctly applied\.

### A\.7Proof of Theorem 3: Four Explicit Individual\-Necessity Witnesses

Theorem 3\.Within the natural lifecycle metadata basis\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\), each component is individually necessary\.

#### A\.7\.1Removing category labelscc

Let a scorerggobserve only\(σ,Δ​t,κ,ξ,h\)\(\\sigma,\\Delta t,\\kappa,\\xi,h\)\. Consider two visible feature vectors

u=\(0\.99,180,κ0,active,∅\),v=\(0\.92,1,κ0,active,∅\)\.u=\(0\.99,180,\\kappa\_\{0\},\\texttt\{active\},\\varnothing\),\\qquad v=\(0\.92,1,\\kappa\_\{0\},\\texttt\{active\},\\varnothing\)\.\(31\)
*Intent 1: numeric preservation\.*The older edgeuuis a Financial fact \(e\.g\., a monthly cost\) and should outrank the newer distractorvv:

*Intent 2: logistical suppression\.*The same visible tuples now correspond to a Logistical conflict in which the newer edgevvshould outrank the stale oneuu:

*Contradiction\.*Becauseggdoes not observecc, it must assign fixed scoresg⁡\(u\)g\(u\)andg⁡\(v\)g\(v\)\. Ifg⁡\(u\)≥g⁡\(v\)g\(u\)\\geq g\(v\), then \([33](https://arxiv.org/html/2609.10413#A1.E33)\) fails\. Ifg⁡\(v\)\>g⁡\(u\)g\(v\)\>g\(u\), then \([32](https://arxiv.org/html/2609.10413#A1.E32)\) fails\. Hence no suchggcan satisfy both intents\. ∎

##### Connection to the measuredα\\alphabounds\.

The same contradiction appears empirically in the scalar familysα=α​a\+\(1−α\)​σs\_\{\\alpha\}=\\alpha a\+\(1\-\\alpha\)\\sigma: on FR\-Graphiti, preservation requiresα≤0\.065\\alpha\\leq 0\.065in the median case while suppression requiresα≥0\.138\\alpha\\geq 0\.138; on FR\-Bank the same conflict is far wider \(min⁡αFmax=1\.7×10−6\\min\\alpha\_\{F\}^\{\\max\}=1\.7\\times 10^\{\-6\}againstmax⁡αLmin≈1\.0\\max\\alpha\_\{L\}^\{\\min\}\\approx 1\.0; §[A\.10](https://arxiv.org/html/2609.10413#A1.SS10)\)\.

#### A\.7\.2Removing slot keysκ\\kappa

Let a supersession ruleDDobserve only\(σ,Δ​t,c,ξ,h\)\(\\sigma,\\Delta t,c,\\xi,h\)for an earlier edge and a later edge\. Take visible tuples

u=\(0\.93,30,Pref,active,∅\),v=\(0\.95,1,Pref,active,∅\)\.u=\(0\.93,30,\\texttt\{Pref\},\\texttt\{active\},\\varnothing\),\\qquad v=\(0\.95,1,\\texttt\{Pref\},\\texttt\{active\},\\varnothing\)\.\(34\)
*HistoryHsameH\_\{\\mathrm\{same\}\}\.*The edges share a slot:κu=κv=\(user,food\_pref\)\\kappa\_\{u\}=\\kappa\_\{v\}=\(\\texttt\{user\},\\texttt\{food\\\_pref\}\)\. The later edge should supersede the earlier one, so the correct deletion action is

*HistoryHdiffH\_\{\\mathrm\{diff\}\}\.*The edges do not share a slot:κu=\(user,food\_pref\)\\kappa\_\{u\}=\(\\texttt\{user\},\\texttt\{food\\\_pref\}\),κv=\(office\_party,catering\)\\kappa\_\{v\}=\(\\texttt\{office\\\_party\},\\texttt\{catering\}\)\. Both edges should survive, so the correct deletion action is

*Contradiction\.*The observed tuples in \([34](https://arxiv.org/html/2609.10413#A1.E34)\) are identical in the two histories, so a rule that does not observeκ\\kappamust return the same valueD⁡\(u,v\)D\(u,v\)in both cases\. Either it over\-deletes \(D=1D=1inHdiffH\_\{\\mathrm\{diff\}\}\) or under\-deletes \(D=0D=0inHsameH\_\{\\mathrm\{same\}\}\)\. Hence slot keys are necessary\. ∎

#### A\.7\.3Removing lifecycle stateξ\\xi

Let a scorerggobserve only\(σ,Δ​t,c,κ,h\)\(\\sigma,\\Delta t,c,\\kappa,h\)\. Take two edges in the same slot:

e1=\(0\.95,30,Pref,food\_pref,∅\),e2=\(0\.95,1,Pref,food\_pref,∅\)\.e\_\{1\}=\(0\.95,30,\\texttt\{Pref\},\\texttt\{food\\\_pref\},\\varnothing\),\\qquad e\_\{2\}=\(0\.95,1,\\texttt\{Pref\},\\texttt\{food\\\_pref\},\\varnothing\)\.\(37\)Consider two intents:qcurq\_\{\\mathrm\{cur\}\}“What does the user currently prefer?” andqchgq\_\{\\mathrm\{chg\}\}“What did the user change from?” Assume strict intent\-opacity:

σ⁡\(ej,qcur\)=σ⁡\(ej,qchg\)=0\.95,j∈\{1,2\}\.\\sigma\(e\_\{j\},q\_\{\\mathrm\{cur\}\}\)=\\sigma\(e\_\{j\},q\_\{\\mathrm\{chg\}\}\)=0\.95,\\qquad j\\in\\\{1,2\\\}\.\(38\)The correct rankings are opposite:

qcur:e2≻e1,qchg:e1≻e2\.q\_\{\\mathrm\{cur\}\}:\\ e\_\{2\}\\succ e\_\{1\},\\qquad q\_\{\\mathrm\{chg\}\}:\\ e\_\{1\}\\succ e\_\{2\}\.\(39\)Becauseggsees identical inputs under both intents, it induces one fixed ordering that violates one of the requirements in \([39](https://arxiv.org/html/2609.10413#A1.E39)\)\. Hence lifecycle state is necessary\. ∎

#### A\.7\.4Removing event\-time anchorshh

Let a scorerggobserve only\(σ,Δ​t,c,κ,ξ\)\(\\sigma,\\Delta t,c,\\kappa,\\xi\)\. Take two obligation edges with identical visible metadata:

e1\\displaystyle e\_\{1\}=\(0\.92,1,Obl,dentist,active,h1=t\+2​d\),\\displaystyle=\(0\.92,1,\\texttt\{Obl\},\\texttt\{dentist\},\\texttt\{active\},h\_\{1\}=t\+2\\text\{d\}\),\(40\)e2\\displaystyle e\_\{2\}=\(0\.92,1,Obl,dentist,active,h2=t−30​d\)\.\\displaystyle=\(0\.92,1,\\texttt\{Obl\},\\texttt\{dentist\},\\texttt\{active\},h\_\{2\}=t\-30\\text\{d\}\)\.\(41\)Consider two intents:qupq\_\{\\mathrm\{up\}\}“What upcoming obligation is relevant?” andqpastq\_\{\\mathrm\{past\}\}“What obligation already passed?” The correct rankings are

qup:e1≻e2,qpast:e2≻e1\.q\_\{\\mathrm\{up\}\}:\\ e\_\{1\}\\succ e\_\{2\},\\qquad q\_\{\\mathrm\{past\}\}:\\ e\_\{2\}\\succ e\_\{1\}\.\(42\)Withouthh, the scorer receives identical visible inputs for both edges and both intents, so it must output one fixed ordering that fails one of the requirements in \([42](https://arxiv.org/html/2609.10413#A1.E42)\)\. Hence event\-time anchors are necessary\. ∎

The witness uses identicalΔ​t\\Delta tfor clarity\. In realistic scenarios, upcoming and expired obligations may have correlated but non\-identical creation ages; theε\\varepsilon\-relaxation of Theorem A\.1 shows that smallΔ​t\\Delta tdifferences do not help when the margin condition holds\.

##### Interpretive remark\.

These witnesses establish necessity only within the natural lifecycle metadata basis\. An alternative encoding is allowed, but it must still transmit the same information\.

### A\.8Proof of Event\-Time Oblivion \(Theorem 3′\)

Theorem 3′\.A memory system is*event\-time\-invariant*if, for every pair of historiesH,H′H,H^\{\\prime\}that differ only in event\-time anchorsheh\_\{e\}\(preserving surface content, semantic similarities, ages, categories, slot keys, and lifecycle states\), the system’s retrieval output is identical\. Under this condition, there exists an obligation\-query distribution on which the system’s error probability is at least1/21/2\.

###### Proof\.

Construct two lifecycle instancesI\+I^\{\+\}andI−I^\{\-\}, each containing one obligation edgeeeand one distractor edgedd\. Agree on all surface features and let

he​\(I\+\)=t\+u,he​\(I−\)=t−u,u\>0\.h\_\{e\}\(I^\{\+\}\)=t\+u,\\qquad h\_\{e\}\(I^\{\-\}\)=t\-u,\\qquad u\>0\.\(43\)For an obligation\-salient queryqq, the correct rankings are

y⁡\(I\+\):e≻d\(upcoming obligation is relevant\),y⁡\(I−\):d≻e\(expired obligation is suppressed\)\.y\(I^\{\+\}\):\\ e\\succ d\\quad\\text\{\(upcoming obligation is relevant\)\},\\qquad y\(I^\{\-\}\):\\ d\\succ e\\quad\\text\{\(expired obligation is suppressed\)\}\.\(44\)Event\-time invariance forces the same output onI\+I^\{\+\}andI−I^\{\-\}\. Therefore the system assigns one fixed ranking that satisfies exactly one of the two correct labels in \([44](https://arxiv.org/html/2609.10413#A1.E44)\)\. Under the uniform distribution over\{I\+,I−\}\\\{I^\{\+\},I^\{\-\}\\\},Pe=1/2P\_\{e\}=1/2\. ∎

##### Scope\.

The result applies to every scorer whose temporal feature isΔ​t\\Delta tor any function ofΔ​t\\Delta talone: such scorers are event\-time\-invariant\. Proposition 2 \(monotone age\-only kernels cannot represent anticipatory activation\) is the kernel\-level statement\. Theorem 3′is the action\-space analog: it lifts the impossibility from scalar activation functions to any deterministic retrieval pipeline whose effects do not depend on the sign oft−het\-h\_\{e\}\.

### A\.9Proof of Retraction Oblivion \(Theorem 3′′\)

##### Scope\.

The theorem applies to systems whose retrieval pipeline treats all stored entries as equally query\-eligible—i\.e\., systems where storage state is binary \(present/absent\) and retrieval does not condition on lifecycle metadata\. A system that stores retraction flags via UPDATE and conditions retrieval on those flags has implicitly implemented a lifecycle state variable; such a system is*not*binary\-flat in our sense\. Empirically, Mem0 and Memory\-R1 both exhibit≈90%\{\\approx\}\\,90\\%AV7 confabulation on LifecycleBench, confirming the binary\-flat characterization: UPDATE overwrites content rather than installing an inactive\-but\-retained state, and retrieval does not distinguish retraction from ordinary presence\.

Theorem 3′′\.A memory system is*binary\-flat retraction\-oblivious*if every stored propositionzzadmits onlyrt​\(z\)∈\{0,1\}r\_\{t\}\(z\)\\in\\\{0,1\\\}\(present/absent\) and retrieval does not gate on lifecycle metadata\. For such a system, under a uniform mixture of current\-state and change\-aware query intents, every binary\-flat strategy has Bayes error exactly1/21/2\.

###### Proof\.

Letzzbe a proposition retracted at timeτ<t\\tau<t\. The two query intents

qcur:“what is currently true?”,qchg:“what did the user retract?”q\_\{\\mathrm\{cur\}\}:\\ \\text\{\`\`what is currently true?''\},\\qquad q\_\{\\mathrm\{chg\}\}:\\ \\text\{\`\`what did the user retract?''\}\(45\)impose

ycur​\(z\)=0,ychg​\(z\)=1\.y\_\{\\mathrm\{cur\}\}\(z\)=0,\\qquad y\_\{\\mathrm\{chg\}\}\(z\)=1\.\(46\)The required relevance pattern is\(0,1\)\(0,1\)\.

*Deterministic case\.*Because the system choosesrt​\(z\)∈\{0,1\}r\_\{t\}\(z\)\\in\\\{0,1\\\}deterministically, the induced relevance pattern is either\(0,0\)\(0,0\)\(delete:qcurq\_\{\\mathrm\{cur\}\}correct,qchgq\_\{\\mathrm\{chg\}\}wrong\) or\(1,1\)\(1,1\)\(retain as active:qcurq\_\{\\mathrm\{cur\}\}wrong,qchgq\_\{\\mathrm\{chg\}\}correct\)\. Under the uniform query distribution, both strategies achieve error probability1/21/2\.

*Randomized case\.*If the system retains with probabilityppand deletes with probability1−p1\-p, the per\-query errors areppforqcurq\_\{\\mathrm\{cur\}\}and1−p1\-pforqchgq\_\{\\mathrm\{chg\}\}, giving

Pe​\(p\)=12​p\+12​\(1−p\)=12for every​p∈\[0,1\]\.P\_\{e\}\(p\)=\\tfrac\{1\}\{2\}p\+\\tfrac\{1\}\{2\}\(1\-p\)=\\tfrac\{1\}\{2\}\\qquad\\text\{for every \}p\\in\[0,1\]\.\(47\)The Bayes error under the uniform query distribution is therefore exactly1/21/2for every binary\-flat strategy\. ∎

##### Whatξ\\xibuys\.

The lifecycle stateξ=retracted\\xi=\\mathrm\{retracted\}with the query\-conditioned maskMq​\(ξ\)M\_\{q\}\(\\xi\)realizes the\(0,1\)\(0,1\)pattern:Mqcur​\(retracted\)=0M\_\{q\_\{\\mathrm\{cur\}\}\}\(\\texttt\{retracted\}\)=0andMqchg​\(retracted\)=1M\_\{q\_\{\\mathrm\{chg\}\}\}\(\\texttt\{retracted\}\)=1\. This pattern is unreachable by any binary\-flat representation over the same storage alphabet: the only way to achieve\(0,1\)\(0,1\)is to introduce a representational state that is retained but masked for current\-state retrieval\. Retraction is not deletion, and “learning” a richer behavior within the\{0,1\}\\\{0,1\\\}vocabulary cannot close the gap\.

### A\.10Proof of Theorem 4

The submitted version stated this result in prose; we give the formal statement here, as requested during review\.

###### Theorem 4 \(Calibration feasibility\)\.

Fix a finite set of lifecycle requirements, each of the form “candidateeemust outrank candidatee′e^\{\\prime\}under queryqq” \(a*preservation*constraint wheneeis the durable fact, a*suppression*constraint whene′e^\{\\prime\}is stale\)\. Under the log\-score of Consequence 1, each requirement is a linear inequality in the per\-category parametersθ=\{αc,λc,Fc\}c∈𝒞\\theta=\\\{\\alpha\_\{c\},\\lambda\_\{c\},F\_\{c\}\\\}\_\{c\\in\\mathcal\{C\}\}, so the feasible setΘm\\Theta\_\{m\}is a convex polyhedron\. LetLα=\{θ∈ℝ\|θ\|:αc=α​∀c\}L\_\{\\alpha\}=\\\{\\theta\\in\\mathbb\{R\}^\{\|\\theta\|\}:\\alpha\_\{c\}=\\alpha\\ \\forall c\\\}be the global\-α\\alphaslice\. Then feasibility is not preserved under restriction toLαL\_\{\\alpha\}:Θm≠∅\\Theta\_\{m\}\\neq\\emptysetwhileΘm∩Lα=∅\\Theta\_\{m\}\\cap L\_\{\\alpha\}=\\emptysetwhenever some category pair\(c,c′\)\(c,c^\{\\prime\}\)carries a preservation boundαcmax\\alpha\_\{c\}^\{\\max\}below a suppression boundαc′min\\alpha\_\{c^\{\\prime\}\}^\{\\min\}\. Empirically this holds on99\.8%99\.8\\%of the1,5661\{,\}566measured cross\-pairs, and on all4545populated cells of the category polytope\.

#### A\.10\.1Convexity of the full feasibility region

Recall the log\-score

ℓθ​\(e,q,t\)=β​σ​\(e,q\)−λce​Δ​te\+Fce\+bce​\(q\)\+log⁡Vce​\(t,he\)\+log⁡Ω⁡\(e\)\+log⁡Mq​\(ξe\)\.\\ell\_\{\\theta\}\(e,q,t\)=\\beta\\sigma\(e,q\)\-\\lambda\_\{c\_\{e\}\}\\Delta t\_\{e\}\+F\_\{c\_\{e\}\}\+b\_\{c\_\{e\}\}\(q\)\+\\log V\_\{c\_\{e\}\}\(t,h\_\{e\}\)\+\\log\\Omega\(e\)\+\\log M\_\{q\}\(\\xi\_\{e\}\)\.Fix a pairwise constraint\(ei\+,ei−,qi,ti\)\(e\_\{i\}^\{\+\},e\_\{i\}^\{\-\},q\_\{i\},t\_\{i\}\)with required marginm\>0m\>0\. Then

ℓθ​\(ei\+,qi,ti\)−ℓθ​\(ei−,qi,ti\)=β​Δ​σi−λci\+​Δ​ti\+\+λci−​Δ​ti−\+Fci\+−Fci−\+bci\+​\(qi\)−bci−​\(qi\)\+Ci,\\ell\_\{\\theta\}\(e\_\{i\}^\{\+\},q\_\{i\},t\_\{i\}\)\-\\ell\_\{\\theta\}\(e\_\{i\}^\{\-\},q\_\{i\},t\_\{i\}\)=\\beta\\,\\Delta\\sigma\_\{i\}\-\\lambda\_\{c\_\{i\}^\{\+\}\}\\Delta t\_\{i\}^\{\+\}\+\\lambda\_\{c\_\{i\}^\{\-\}\}\\Delta t\_\{i\}^\{\-\}\+F\_\{c\_\{i\}^\{\+\}\}\-F\_\{c\_\{i\}^\{\-\}\}\+b\_\{c\_\{i\}^\{\+\}\}\(q\_\{i\}\)\-b\_\{c\_\{i\}^\{\-\}\}\(q\_\{i\}\)\+C\_\{i\},\(48\)whereCiC\_\{i\}collects the fixed terms fromVV,Ω\\Omega, andMM\. Equation \([48](https://arxiv.org/html/2609.10413#A1.E48)\) is affine inθ\\theta\. Hence each retrieval constraint has the formai⊤​θ≥m−Cia\_\{i\}^\{\\top\}\\theta\\geq m\-C\_\{i\}for some vectoraia\_\{i\}\. Therefore

Θm=⋂i=1n\{θ:ai⊤​θ≥m−Ci\}\\Theta\_\{m\}=\\bigcap\_\{i=1\}^\{n\}\\left\\\{\\theta:\\ a\_\{i\}^\{\\top\}\\theta\\geq m\-C\_\{i\}\\right\\\}\(49\)is an intersection of halfspaces and is therefore convex\. ∎

#### A\.10\.2Global\-α\\alphainfeasibility as a one\-dimensional slice

Now consider the simplified blended scoresα​\(e,q\)=α​a​\(e\)\+\(1−α\)​σ​\(e,q\)s\_\{\\alpha\}\(e,q\)=\\alpha a\(e\)\+\(1\-\\alpha\)\\sigma\(e,q\)\.

*Preservation constraint\.*Letffbe an old but correct fact anddda newer distractor such thataf<ada\_\{f\}<a\_\{d\}andσf\>σd\\sigma\_\{f\}\>\\sigma\_\{d\}\. Requiringffto outrankddgives

α​af\+\(1−α\)​σf\\displaystyle\\alpha a\_\{f\}\+\(1\-\\alpha\)\\sigma\_\{f\}≥α​ad\+\(1−α\)​σd\\displaystyle\\geq\\alpha a\_\{d\}\+\(1\-\\alpha\)\\sigma\_\{d\}α⁡\(ad−af\)\\displaystyle\\alpha\(a\_\{d\}\-a\_\{f\}\)≤\(1−α\)​\(σf−σd\)\\displaystyle\\leq\(1\-\\alpha\)\(\\sigma\_\{f\}\-\\sigma\_\{d\}\)α\\displaystyle\\alpha≤σf−σd\(σf−σd\)\+\(ad−af\)=αFmax\.\\displaystyle\\leq\\frac\{\\sigma\_\{f\}\-\\sigma\_\{d\}\}\{\(\\sigma\_\{f\}\-\\sigma\_\{d\}\)\+\(a\_\{d\}\-a\_\{f\}\)\}=\\alpha\_\{F\}^\{\\max\}\.\(50\)
*Suppression constraint\.*Letxxbe the correct current fact andyya stale but semantically attractive distractor such thatax\>aya\_\{x\}\>a\_\{y\}andσy\>σx\\sigma\_\{y\}\>\\sigma\_\{x\}\. Requiringxxto outrankyygives

α​ax\+\(1−α\)​σx\\displaystyle\\alpha a\_\{x\}\+\(1\-\\alpha\)\\sigma\_\{x\}≥α​ay\+\(1−α\)​σy\\displaystyle\\geq\\alpha a\_\{y\}\+\(1\-\\alpha\)\\sigma\_\{y\}α\\displaystyle\\alpha≥σy−σx\(σy−σx\)\+\(ax−ay\)=αLmin\.\\displaystyle\\geq\\frac\{\\sigma\_\{y\}\-\\sigma\_\{x\}\}\{\(\\sigma\_\{y\}\-\\sigma\_\{x\}\)\+\(a\_\{x\}\-a\_\{y\}\)\}=\\alpha\_\{L\}^\{\\min\}\.\(51\)
If

αLmin\>αFmax,\\alpha\_\{L\}^\{\\min\}\>\\alpha\_\{F\}^\{\\max\},\(52\)the feasible interval is empty and no globalα\\alphaexists\.

##### Measured witness\.

MedianαFmax=0\.065\\alpha\_\{F\}^\{\\max\}=0\.065and medianαLmin=0\.138\\alpha\_\{L\}^\{\\min\}=0\.138yield70\.9%70\.9\\%infeasible cross\-pairs on FR\-Graphiti\. On FR\-Bank \(n=54n=54AV8 preservation bounds,n=29n=29AV2 suppression bounds\), the global\-α\\alphaconflict tightens:min⁡αFmax=1\.7×10−6\\min\\alpha\_\{F\}^\{\\max\}=1\.7\\times 10^\{\-6\},max⁡αLmin≈1\.0\\max\\alpha\_\{L\}^\{\\min\}\\approx 1\.0, feasibility gap≈1\.0\\approx 1\.0, and99\.8%99\.8\\%of cross\-pair constraints are infeasible\. Moreover, the11×1111\\times 11cross\-category polytope has zero feasible cells among its4545populated cells \(55diagonal,4040off\-diagonal\): no singleα\\alphasatisfies both a preservation constraint of any category and a suppression constraint of any other\. \(The submitted version described these4545cells as off\-diagonal; the artifact records4545populated cells in total\.\)

#### A\.10\.3Category\-specific expansion and anti\-squatting

With category\-specific blending weights, the scalar interval becomes a Cartesian product:

Θα=∏c∈𝒞\[α¯c,α¯c\]\.\\Theta\_\{\\alpha\}=\\prod\_\{c\\in\\mathcal\{C\}\}\[\\underline\{\\alpha\}\_\{c\},\\overline\{\\alpha\}\_\{c\}\]\.\(53\)This product may be nonempty even when the global one\-dimensional interval is empty\.

Anti\-squatting constraints are encoded as ordinary pairwise inequalities\. Ifere\_\{r\}is the relevant edge for queryqqandese\_\{s\}is a slow\-decay “squatter” from a category such as Identity, then

ℓθ​\(er,q,t\)−ℓθ​\(es,q,t\)≥m\.\\ell\_\{\\theta\}\(e\_\{r\},q,t\)\-\\ell\_\{\\theta\}\(e\_\{s\},q,t\)\\geq m\.\(54\)If Identity decay is too slow or its floor too high, constraints of the form \([54](https://arxiv.org/html/2609.10413#A1.E54)\) are violated\. This is exactly what occurred under the earlier800×800\\timesrate spread: Identity occupied64%64\\%of top\-5 slots regardless of query\. Compressing to a5\.3×5\.3\\timesspread restored feasibility\.

### A\.11Dimensional Necessity of Category\-Specific Parameters

Theorem 4 shows the feasible polyhedronΘm\\Theta\_\{m\}is convex and that the global\-α\\alphaslice can be empty\. The following claim explains*why*a low\-dimensional parameter family is structurally insufficient\.

Claim \(dimensional necessity\)\.Letp=2​K\+1p=2K\+1be the full parameter count forθ=\(β,\{λc,Fc\}c∈𝒞\)\\theta=\(\\beta,\\\{\\lambda\_\{c\},F\_\{c\}\\\}\_\{c\\in\\mathcal\{C\}\}\), and letgc​\(θ\)=rc⊤​θ\+scg\_\{c\}\(\\theta\)=r\_\{c\}^\{\\top\}\\theta\+s\_\{c\},c=1,…,Kc=1,\\ldots,K, be category\-specific margin functionals whose gradient matrixG=\[r1,…,rK\]⊤∈ℝK×pG=\[r\_\{1\},\\ldots,r\_\{K\}\]^\{\\top\}\\in\\mathbb\{R\}^\{K\\times p\}has rankKK\. AssumeΘm\\Theta\_\{m\}is strictly feasible \(contains an open ball\)\. IfL⊆ℝpL\\subseteq\\mathbb\{R\}^\{p\}is any affine subspace withdim\(L\)<K\\dim\(L\)<K, then the imageg⁡\(L\)g\(L\)has Lebesgue measure zero inℝK\\mathbb\{R\}^\{K\}, so for Lebesgue\-almost every targetτ∈g⁡\(Θm\)\\tau\\in g\(\\Theta\_\{m\}\)there is noθ∈L∩Θm\\theta\\in L\\cap\\Theta\_\{m\}withg⁡\(θ\)=τg\(\\theta\)=\\tau\. In particular, a one\-dimensional global\-α\\alphafamily is generically infeasible for independently perturbed category\-margin targets wheneverK\>1K\>1\.

##### Sketch\.

By strict feasibility and surjectivity ofGG,g⁡\(Θm\)g\(\\Theta\_\{m\}\)contains an open set inℝK\\mathbb\{R\}^\{K\}\. ForLLaffine withdim\(L\)=d<K\\dim\(L\)=d<K,g⁡\(L\)g\(L\)is affine withdim\(g⁡\(L\)\)≤d<K\\dim\(g\(L\)\)\\leq d<Kand therefore hasKK\-dimensional Lebesgue measure zero; almost everyτ∈g⁡\(Θm\)\\tau\\in g\(\\Theta\_\{m\}\)escapesg⁡\(L\)g\(L\)\. The operational content matches the empirical99\.8%99\.8\\%cross\-pair infeasibility on FR\-Bank and the zero feasible cells in the11×1111\\times 11cross\-category polytope \(Theorem 4 empirical witness\): a one\-dimensional parameter family cannot span an1111\-dimensional category\-margin space, and category\-specific\{αc,λc,Fc\}\\\{\\alpha\_\{c\},\\lambda\_\{c\},F\_\{c\}\\\}are the coordinates that do\.

### A\.12Staleness Decomposition: Derivation and Numerical Predictions

We restate the staleness decomposition introduced in Section[4](https://arxiv.org/html/2609.10413#S4)and record its derivation\. LetBBdenote the event that the retrieved set contains stale harmful context and letπS=PS​\(B=1\)\\pi\_\{S\}=P\_\{S\}\(B=1\)for systemSS\. Conditioning onBBgives

PS​\(pass\)=P⁡\(pass∣B=0\)​PS​\(B=0\)\+P⁡\(pass∣B=1\)​PS​\(B=1\)=\(1−πS\)​p0\+πS​p1,P\_\{S\}\(\\mathrm\{pass\}\)=P\(\\mathrm\{pass\}\\mid B=0\)P\_\{S\}\(B=0\)\+P\(\\mathrm\{pass\}\\mid B=1\)P\_\{S\}\(B=1\)=\(1\-\\pi\_\{S\}\)p\_\{0\}\+\\pi\_\{S\}p\_\{1\},\(55\)which is the staleness decomposition stated in §[4](https://arxiv.org/html/2609.10413#S4)\. Subtracting between two systemsAAandBB,

PA​\(pass\)−PB​\(pass\)=\(πB−πA\)​p0\+\(πA−πB\)​p1=\(πB−πA\)​\(p0−p1\),P\_\{A\}\(\\mathrm\{pass\}\)\-P\_\{B\}\(\\mathrm\{pass\}\)=\(\\pi\_\{B\}\-\\pi\_\{A\}\)p\_\{0\}\+\(\\pi\_\{A\}\-\\pi\_\{B\}\)p\_\{1\}=\(\\pi\_\{B\}\-\\pi\_\{A\}\)\(p\_\{0\}\-p\_\{1\}\),\(56\)which is the across\-system gap form\. The algebraic step is one line; the substantive content is empirical: the calibration ofp0,p1p\_\{0\},p\_\{1\}\(and the analogousc0,c1c\_\{0\},c\_\{1\}below\) and the contamination gapsπA−πB\\pi\_\{A\}\-\\pi\_\{B\}between systems\.

##### Numerical example\.

Using the reported clean\-vs\-contaminated pass rates,p0=0\.758p\_\{0\}=0\.758,p1=0\.060p\_\{1\}=0\.060\. Comparing FR\-Graphiti \(πA=0\.08\\pi\_\{A\}=0\.08\) to Mem0 \(πB=0\.27\\pi\_\{B\}=0\.27\),

PA​\(pass\)−PB​\(pass\)=\(0\.27−0\.08\)​\(0\.758−0\.060\)=0\.19×0\.698≈0\.1326,P\_\{A\}\(\\mathrm\{pass\}\)\-P\_\{B\}\(\\mathrm\{pass\}\)=\(0\.27\-0\.08\)\(0\.758\-0\.060\)=0\.19\\times 0\.698\\approx 0\.1326,predicting a13\.313\.3pp pass advantage from contamination reduction alone, close to the observed1212pp retrieval gap\.

##### Confabulation analogue\.

Ifc0=P⁡\(confab∣B=0\)c\_\{0\}=P\(\\mathrm\{confab\}\\mid B=0\)andc1=P⁡\(confab∣B=1\)c\_\{1\}=P\(\\mathrm\{confab\}\\mid B=1\), thenPS​\(confab\)=\(1−πS\)​c0\+πS​c1P\_\{S\}\(\\mathrm\{confab\}\)=\(1\-\\pi\_\{S\}\)c\_\{0\}\+\\pi\_\{S\}c\_\{1\}, soPB​\(confab\)−PA​\(confab\)=\(πB−πA\)​\(c1−c0\)\.P\_\{B\}\(\\mathrm\{confab\}\)\-P\_\{A\}\(\\mathrm\{confab\}\)=\(\\pi\_\{B\}\-\\pi\_\{A\}\)\(c\_\{1\}\-c\_\{0\}\)\.This explains why FR’s staleness reduction maps directly to the observed confabulation gap \(22\.4%22\.4\\%vs45\.1%45\.1\\%against Mem0\)\.

##### Staleness transfer: a testable invariant and its falsification \(Proposition 3A\)\.

If\(p0,p1\)\(p\_\{0\},p\_\{1\}\)are system\-invariant \(Assumption 3A\), then \([55](https://arxiv.org/html/2609.10413#A1.E55)\) becomes a predictive model: each systemSSsatisfiesPS=p0−πS​\(p0−p1\)P\_\{S\}=p\_\{0\}\-\\pi\_\{S\}\(p\_\{0\}\-p\_\{1\}\), so held\-out pass rates are predictable from staleness rates alone\. Calibratingδ=p0−p1\\delta=p\_\{0\}\-p\_\{1\}from FR\-Graphiti \(π=0\.08\\pi=0\.08,P=0\.73P=0\.73\) and Mem0 \(π=0\.27\\pi=0\.27,P=0\.61P=0\.61\) gives

δ=0\.73−0\.610\.27−0\.08=0\.632,p0=0\.73\+0\.08⋅0\.632=0\.780,p1=0\.148\.\\delta=\\frac\{0\.73\-0\.61\}\{0\.27\-0\.08\}=0\.632,\\qquad p\_\{0\}=0\.73\+0\.08\\cdot 0\.632=0\.780,\\qquad p\_\{1\}=0\.148\.\(57\)The predicted pass rateP^S=p0−πS​δ\\widehat\{P\}\_\{S\}=p\_\{0\}\-\\pi\_\{S\}\\deltaon three held\-out systems \(reference values from Table[3](https://arxiv.org/html/2609.10413#S6.T3)\):

SystemπS\\pi\_\{S\}P^S\\widehat\{P\}\_\{S\}\|PS−P^S\|\|P\_\{S\}\-\\widehat\{P\}\_\{S\}\|FR\-Bank0\.1550\.1550\.6830\.6838\.6​pp\\mathbf\{8\.6\\text\{ pp\}\}Memory\-R10\.1530\.1530\.6840\.6841\.5​pp1\.5\\text\{ pp\}MemoryOS0\.0700\.0700\.7360\.7363\.1​pp3\.1\\text\{ pp\}
FR\-Bank and Memory\-R1 have all but identical staleness \(π=0\.155\\pi=0\.155vs\.0\.1530\.153, a0\.20\.2pp difference\) yet their pass rates differ by10\.010\.0pp—a gap impossible under Assumption 3A, which makes pass rate a function ofπ\\pialone\. Hence Assumption 3A is empirically*falsified*\. Clean\-context recall qualityp0p\_\{0\}is system\-dependent, so recall quality is a second mechanism orthogonal to staleness filtering\. The identity \([55](https://arxiv.org/html/2609.10413#A1.E55)\) remains exact, but it is not a sufficient predictor: staleness rate captures one of two orthogonal mechanisms that determine pass rate\. FR\-Bank’s76\.9%76\.9\\%pass rate derives from both low staleness \(π=0\.155\\pi=0\.155\) and high clean\-context recall, not from staleness alone\.

### A\.13Anticipatory Activation and Why Age Alone Cannot Express It

Proposition 2\.No monotone nonincreasing function of edge age can represent anticipatory activation\.

###### Proof\.

Suppose for contradiction that there exists a nonincreasing functiong:ℝ≥0→ℝg:\\mathbb\{R\}\_\{\\geq 0\}\\to\\mathbb\{R\}such that edge relevance can be written asu⁡\(t\)=g⁡\(t−te\)u\(t\)=g\(t\-t\_\{e\}\), wheretet\_\{e\}is creation time\. Take timest1<t2<ht\_\{1\}<t\_\{2\}<h, wherehhis the event time\. Becauset1−te<t2−tet\_\{1\}\-t\_\{e\}<t\_\{2\}\-t\_\{e\}andggis nonincreasing,

u⁡\(t1\)=g⁡\(t1−te\)≥g⁡\(t2−te\)=u⁡\(t2\)\.u\(t\_\{1\}\)=g\(t\_\{1\}\-t\_\{e\}\)\\geq g\(t\_\{2\}\-t\_\{e\}\)=u\(t\_\{2\}\)\.\(58\)But anticipatory activation requires relevance to*increase*as the event approaches from the left:

u⁡\(t1\)<u⁡\(t2\)for​t1<t2<h\.u\(t\_\{1\}\)<u\(t\_\{2\}\)\\qquad\\text\{for \}t\_\{1\}<t\_\{2\}<h\.\(59\)Equations \([58](https://arxiv.org/html/2609.10413#A1.E58)\) and \([59](https://arxiv.org/html/2609.10413#A1.E59)\) are contradictory\. Therefore no monotone nonincreasing function of age alone can represent anticipatory activation\. ∎

##### Why the FR kernel works\.

ForVc​\(t,h\)=exp⁡\[−νc​\(h−t\)\+\]​exp​\[−μc​\(t−h\)\+\]V\_\{c\}\(t,h\)=\\exp\[\-\\nu\_\{c\}\(h\-t\)\_\{\+\}\]\\,\\exp\[\-\\mu\_\{c\}\(t\-h\)\_\{\+\}\]withμc≫νc\\mu\_\{c\}\\gg\\nu\_\{c\}: ift<ht<h,Vc​\(t,h\)=exp⁡\[−νc​\(h−t\)\]V\_\{c\}\(t,h\)=\\exp\[\-\\nu\_\{c\}\(h\-t\)\], with derivativeνc​exp⁡\[−νc​\(h−t\)\]\>0\\nu\_\{c\}\\exp\[\-\\nu\_\{c\}\(h\-t\)\]\>0, so relevance increases as the event approaches; ift\>ht\>h,Vc​\(t,h\)=exp⁡\[−μc​\(t−h\)\]V\_\{c\}\(t,h\)=\\exp\[\-\\mu\_\{c\}\(t\-h\)\], with derivative−μc​exp⁡\[−μc​\(t−h\)\]<0\-\\mu\_\{c\}\\exp\[\-\\mu\_\{c\}\(t\-h\)\]<0, so relevance decreases after expiry\. The FR kernel has the qualitatively correct shape that an age\-only decay cannot reproduce\.

### A\.14Proof of Lemma 1 \(Harmonic\-Mean Decay\)

Letτc=1/λc\\tau\_\{c\}=1/\\lambda\_\{c\}denote the persistence timescale of categorycc\. Assume soft membershipswc​\(e\)≥0w\_\{c\}\(e\)\\geq 0satisfy∑cwc​\(e\)=1\\sum\_\{c\}w\_\{c\}\(e\)=1and that timescales average linearly:

τeff​\(e\)=∑cwc​\(e\)​τc\.\\tau\_\{\\mathrm\{eff\}\}\(e\)=\\sum\_\{c\}w\_\{c\}\(e\)\\tau\_\{c\}\.\(60\)Substitutingτc=1/λc\\tau\_\{c\}=1/\\lambda\_\{c\}givesτeff​\(e\)=∑cwc​\(e\)/λc\\tau\_\{\\mathrm\{eff\}\}\(e\)=\\sum\_\{c\}w\_\{c\}\(e\)/\\lambda\_\{c\}\. Sinceλeff​\(e\)=1/τeff​\(e\)\\lambda\_\{\\mathrm\{eff\}\}\(e\)=1/\\tau\_\{\\mathrm\{eff\}\}\(e\),

λeff​\(e\)=\(∑cwc​\(e\)λc\)−1\.\\lambda\_\{\\mathrm\{eff\}\}\(e\)=\\left\(\\sum\_\{c\}\\frac\{w\_\{c\}\(e\)\}\{\\lambda\_\{c\}\}\\right\)^\{\-1\}\.\(61\)This is the harmonic mean\. ∎

##### Numerical example\.

For30%30\\%Identity and70%70\\%Logistical membership,

λeff=\(0\.30\.0015\+0\.70\.0080\)−1≈0\.00348/hr\.\\lambda\_\{\\mathrm\{eff\}\}=\\left\(\\frac\{0\.3\}\{0\.0015\}\+\\frac\{0\.7\}\{0\.0080\}\\right\)^\{\-1\}\\approx 0\.00348/\\mathrm\{hr\}\.The corresponding half\-life ist1/2=ln⁡2/λeff≈199\.3t\_\{1/2\}=\\ln 2/\\lambda\_\{\\mathrm\{eff\}\}\\approx 199\.3hr≈8\.3\\approx 8\.3days\.

##### Soft membership in practice\.

On the full FR\-Bank corpus \(12,96812\{,\}968active entries across4040persona banks\),66\.8%66\.8\\%of entries have primary category weight below0\.900\.90\(28\.7%28\.7\\%below0\.800\.80\), and the mean number of categories with weight\>0\.05\>0\.05per entry is2\.02\.0\. Harmonic\-mean decay therefore fires on the majority of the corpus, not as a theoretical edge case\. The most frequent co\-occurrence pairs are Intellectual Interests↔\\leftrightarrowProjects & Endeavors \(635635entries\), Health & Wellbeing↔\\leftrightarrowObligations \(438438\), and Projects & Endeavors↔\\leftrightarrowRelational Bonds \(422422\), reflecting genuine behavioral ambiguity: a research project involves both intellectual engagement and deliverable\-tracking, while a chronic health condition generates both ongoing state and time\-bound medical obligations\.

### A\.15Final Interpretation

The theory supports a precise and limited claim:

- •Model 1 motivates the feature set\.
- •Theorem 1 proves that\(σ,Δ​t\)\(\\sigma,\\Delta t\)alone does not identify lifecycle state\.
- •Theorem 2 shows that FR’s metadata are sufficient under the model, and Theorem 2′strengthens this to minimality: no strict subset of\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)resolves all lifecycle failures\.
- •Theorem 3 shows that each metadata field is individually necessary within the natural lifecycle basis\. Theorems 3′and 3′′lift this into action\-space impossibility: event\-time\-invariant and binary\-flat retraction\-oblivious action spaces have worst\-case error≥1/2\\geq 1/2on their respective query distributions\.
- •Theorem 4 shows that calibration is a convex feasibility problem, and that globalα\\alphafails because it is an overly restrictive one\-dimensional slice\. Theorem 2A gives a provable lower bound on the variance gap between behavioral and cognitive partitions, at least10%10\\%ofV⁡\(𝒞uniform\)V\(\\mathcal\{C\}\_\{\\mathrm\{uniform\}\}\)on our tables\.
- •The staleness decomposition \(\([55](https://arxiv.org/html/2609.10413#A1.E55)\)–\([56](https://arxiv.org/html/2609.10413#A1.E56)\)\) shows that stale context has negative expected utility\. Proposition 3A tests its strongest form—system\-invariance of\(p0,p1\)\(p\_\{0\},p\_\{1\}\)—and falsifies it via the FR\-Bank/Memory\-R1 natural experiment, identifying clean\-context recall quality as a second orthogonal mechanism\.

None of these results requires claiming that FR performs Bayesian inference at runtime\. FR is a deterministic lifecycle policy whose feature set can be interpreted as the sufficient\-statistic basis of a lifecycle\-aware active\-relevance model\.

### A\.16Theory Summary

Table 6:Theoretical results and the mechanisms they justify\.ResultClaimMechanism justifiedModel 1Lifecycle posterior decomposes into category, slot, state, event\-time factorsFull FR feature setTheorem 1\(σ,Δ​t\)\(\\sigma,\\Delta t\)\-only scoring cannot identify lifecycle stateSlot keys \+ supersession \+ classifier \+ event\-timeTheorem 2\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)is sufficient under Model 1FR metadata basisTheorem 2′No strict subset of\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)resolves all lifecycle failure modesFR metadata basis \(minimality\)Theorem 3Each of\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)is individually necessaryAll four mechanismsTheorem 3′Event\-time\-invariant action spaces:Pe≥1/2P\_\{e\}\\geq 1/2on obligationsEvent\-time anchors as action coordTheorem 3′′Binary\-flat retraction\-oblivious spaces: BayesPe=1/2P\_\{e\}=1/2Lifecycle stateξ\\xias retention gateTheorem 4Calibration is convex feasibility; globalα\\alphacan be infeasibleCategory\-specific parametersProposition 1Behavioral ontology minimizes within\-category policy variance10\+1 ontologyTheorem 2APartition gapV⁡\(𝒞cog\)−V⁡\(𝒞beh\)≥10%​V​\(𝒞uniform\)V\(\\mathcal\{C\}\_\{\\mathrm\{cog\}\}\)\-V\(\\mathcal\{C\}\_\{\\mathrm\{beh\}\}\)\\geq 10\\%\\,V\(\\mathcal\{C\}\_\{\\mathrm\{uniform\}\}\)Behavioral partition as variance\-minimizerEq\. \([55](https://arxiv.org/html/2609.10413#A1.E55)\)–\([56](https://arxiv.org/html/2609.10413#A1.E56)\)Stale context has negative expected utility \(decomposition identity\)Lifecycle filteringProposition 3AStaleness transfer falsified:p0p\_\{0\}is system\-dependentStaleness is one of two orthogonal mechanismsProposition 2Age\-only decay cannot express anticipatory activationEvent\-time anchorsLemma 1Soft membership→\\toharmonic\-mean decayMulti\-category classification

## Appendix BExtended Architecture Details

![Refer to caption](https://arxiv.org/html/2609.10413v1/neurips_fig2.png)Figure 2:Two lifecycle mechanisms in detail\.\(A\) Slot\-key supersession with query\-conditioned state mask\. When “I moved to London” is ingested, the high\-confidence contradiction marks the earlier “lives in Istanbul” edge asξ=superseded\\xi=\\texttt\{superseded\}\. The same store returns different answers depending on query intent: current\-state queries applyMq​\(ξ\)M\_\{q\}\(\\xi\)to exclude superseded edges \(returning London\); change\-aware queries include them \(returning Istanbul\)\. \(B\) Event\-time validity for obligations\. Activation is governed by distance to the event\-time anchorhh, not from creation\. Anticipatory activation rises as the deadline approaches; post\-event the validity kernelVc​\(t,h\)V\_\{c\}\(t,h\)collapses, suppressing expired obligations from current\-state queries\. Both mechanisms instantiate dimensions of the metadata basis\(c,κ,ξ,h\)\(c,\\kappa,\\xi,h\)that Theorems 1–3 establish as necessary for lifecycle\-aware scoring\.### B\.1Classifier Iteration

Table 7:Classifier prompt iteration on a 30\-fact development set, scored as strict\-agreement plus half\-credit for primary/secondary swaps\. The 93% figure is the dev\-set prompt\-iteration result and is*not*the canonical classifier quality number; the held\-out audit onn=200n=200facts reports70\.7%70\.7\\%majority\-vote agreement \(κ=\+0\.673\\kappa=\+0\.673, Table[8](https://arxiv.org/html/2609.10413#A2.T8)\)\.VersionKey ChangeDev\-set agreement \(n=30\)v1Initial 8\+1 prompt77%v2“Classify fact, not utterance”Overcorrectedv3Softened to “stored fact” rules87%v4Split to 10\+1 \+ OTHER cap \+ CoT93%#### B\.1\.1Classifier Agreement Audit

To validate classifier quality reproducibly, we conducted a three\-judge blind audit on a 200\-fact stratified sample \(seed=42=42, minimum 5 facts per category\) drawn from the canonical FR\-Bank corpus \(LifecycleBench/artifacts/lifecycle\_banks/,\|E\|=18,936\|E\|=18\{,\}936\)\. Three independent LLM judges—Claude Sonnet 4\.6, GPT\-4o, and GPT\-4\.1\-mini—re\-classified each fact\. Each judge received the full source session as conversation context, matching the SESSION CONTEXT plus CURRENT TURN inputs the ingestion classifier sees\.

Table 8:Three\-judge agreement results with full session context\. Cohen’sκ\\kappaover the 11\-category label set; “Majority vote” aggregates judges by simple plurality \(≥2\\geq 2of 3 agree\)\.ComparisonnnRawCohen’sκ\\kappaclaude\_sonnet vs gpt4o20072\.5%\+0\.689\+0\.689claude\_sonnet vs gpt41\_mini20067\.0%\+0\.626\+0\.626gpt4o vs gpt41\_mini20077\.5%\+0\.744\+0\.744claude\_sonnet vs FR\-Bank20060\.5%\+0\.560\+0\.560gpt4o vs FR\-Bank20067\.0%\+0\.632\+0\.632gpt41\_mini vs FR\-Bank20069\.0%\+0\.653\+0\.653Majority vote vs FR\-Bank18870\.7%\+0\.673\\mathbf\{\+0\.673\}Table 9:Per\-category majority\-vote agreement vs FR\-Bank classifier label, sorted descending\.CategoryAgreementRELATIONAL\_BONDS93\.5%IDENTITY\_SELF\_CONCEPT93\.3%FINANCIAL\_MATERIAL90\.0%HEALTH\_WELLBEING85\.7%PREFERENCES\_HABITS85\.0%HOBBIES\_RECREATION76\.9%PROJECTS\_ENDEAVORS65\.2%LOGISTICAL\_CONTEXT64\.7%OBLIGATIONS41\.4%INTELLECTUAL\_INTERESTS33\.3%##### Per\-category precision, recall, and F1\.

Table[10](https://arxiv.org/html/2609.10413#A2.T10)reports precision, recall, and F1 for each category, treating the three\-judge majority vote as ground truth\. The five categories with the sharpest lifecycle\-policy differences—Relational\_Bonds\(F1=0\.853=0\.853\),Preferences\_Habits\(0\.7910\.791\),Health\_Wellbeing\(0\.7500\.750\),Financial\_Material\(0\.6670\.667\), andHobbies\_Recreation\(0\.6670\.667\)—all exceed F1=0\.65=0\.65, confirming that classification reliability is highest where lifecycle\-policy divergence is greatest\. The two confused pairs targeted by the perturbation study \(Obligations↔\\leftrightarrowLogistical\_Context,Intellectual\_Interests↔\\leftrightarrowProjects\_Endeavors\) show the lowest precision, consistent with the perturbation study \(Appendix[B\.1\.2](https://arxiv.org/html/2609.10413#A2.SS1.SSS2)\) demonstrating that these confusions have negligible downstream impact because the lifecycle policies for each pair are similar\.

Table 10:Per\-category classifier P/R/F1 from the held\-out audit \(n=200n=200; majority vote of three independent judges as ground truth, restricted to facts with a majority verdict,neff=188n\_\{\\mathrm\{eff\}\}=188\)\. Macro\-averaged F1=0\.595=0\.595; weighted F1=0\.647=0\.647; overall accuracy66\.5%66\.5\\%\.CategorynnPrecisionRecallF1RELATIONAL\_BONDS31310\.9350\.9350\.7840\.7840\.853\\mathbf\{0\.853\}PREFERENCES\_HABITS20200\.8500\.8500\.7390\.7390\.7910\.791HEALTH\_WELLBEING15150\.8000\.8000\.7060\.7060\.7500\.750PROJECTS\_ENDEAVORS28280\.5360\.5360\.9380\.9380\.6820\.682FINANCIAL\_MATERIAL10100\.9000\.9000\.5290\.5290\.6670\.667HOBBIES\_RECREATION13130\.7690\.7690\.5880\.5880\.6670\.667IDENTITY\_SELF\_CONCEPT16160\.8750\.8750\.4240\.4240\.5710\.571LOGISTICAL\_CONTEXT18180\.6110\.6110\.5240\.5240\.5640\.564OBLIGATIONS31310\.3870\.3870\.8570\.8570\.5330\.533INTELLECTUAL\_INTERESTS12120\.3330\.3330\.8000\.8000\.4710\.471OTHER6\\phantom\{0\}60\.0000\.0000\.0000\.0000\.0000\.000Discussion\.Four observations from the audit:

1. 1\.Context matters\.A decontextualized audit \(fact text only, no conversation\) yieldsκ=\+0\.58\\kappa=\+0\.58\(vs\.\+0\.67\+0\.67with context\), confirming that behavioral classification requires conversational context\.
2. 2\.Disagreements are concentrated and explicable\.OBLIGATIONS vs\. LOGISTICAL\_CONTEXT reflects the classifier’s deliberate event\-time routing \(facts with date anchors route to OBLIGATIONS for anticipatory activation\)\. PROJECTS\_ENDEAVORS vs\. HOBBIES\_RECREATION reflects the DELIVERABLE TEST override \(§[3](https://arxiv.org/html/2609.10413#S3)\)\. These are policy choices, not errors\.
3. 3\.INTELLECTUAL\_INTERESTS over\-assignment\.Low agreement \(33\.3%\) with full context suggests the classifier may over\-assign this category; tightening this boundary is identified as future work\.
4. 4\.Errors concentrate where lifecycle policies are most similar\.The five categories with the sharpest lifecycle\-policy differences—Identity, Relational, Financial, Health, Preferences—all exceed 85% agreement, indicating that classification errors concentrate where lifecycle policies are most similar and therefore least consequential to retrieval quality\.

Raw per\-fact verdicts and aggregate metrics for both audits are released atartifacts/classifier\_audit\_results\_v2\.jsonandartifacts/classifier\_audit\_summary\_v2\.json\(and\_results\.json/\_summary\.jsonfor the no\-context audit\)\.

To quantify the downstream impact of these category confusions, we conduct a perturbation study in Appendix[B\.1\.2](https://arxiv.org/html/2609.10413#A2.SS1.SSS2)that randomly flips labels between the two confused pairs \(Obligations↔\\leftrightarrowLogistical Context, Intellectual Interests↔\\leftrightarrowProjects & Endeavors\) at rates from 0% to 50% and measures retrieval\-set stability\.

#### B\.1\.2Downstream Sensitivity to Category Perturbation

To quantify downstream sensitivity to classifier disagreement on the two confused category pairs identified in the audit \(Obligations↔\\leftrightarrowLogistical Context, Intellectual Interests↔\\leftrightarrowProjects & Endeavors\), we randomly perturbed category labels at rates from 5% to 50% and measured retrieval\-set stability across all 516 LifecycleBench questions \(3 seeds per rate\)\. At 10% perturbation, mean Jaccard overlap between the original and perturbed top\-10 retrieval sets is0\.9740\.974\(±0\.002\\pm 0\.002\), with an average of0\.290\.29edges displaced per query\. Even at 50% perturbation—equivalent to random assignment within the confused pairs—Jaccard overlap remains0\.9050\.905and Kendallτ\\tauremains0\.8970\.897\. This confirms that classifier errors concentrated among nearby\-policy categories have minimal downstream impact on retrieval quality: the lifecycle policies for these confused pairs are similar enough that swapping labels does not materially alter which facts reach the top\-10\. This stability is predicted by the theoretical framework: Proposition 1 guarantees that confused pairs have minimal within\-category policy variance, Theorem 4 shows that global\-α\\alphainfeasibility \(99\.8% on FR\-Bank\) concentrates on*distant*category pairs, while confused pairs share nearby feasibility intervals, and Lemma 1’s harmonic\-mean decay ensures that soft category membership partially absorbs hard label perturbations\.

Table 11:Retrieval\-set stability under random label flips between the two confused category pairs \(Obligations↔\\leftrightarrowLogistical Context, Intellectual Interests↔\\leftrightarrowProjects & Endeavors\)\. Averaged over 516 LifecycleBench questions and 3 seeds per rate\. Jaccard and displaced are over top\-10 edge IDs; Kendallτ\\tauis over edges present in both rankings \(variantτb\\tau\_\{b\}; undefined when the intersection has fewer than 2 edges\)\. Scoring reproduces the deterministic portion oflifecycle\_search: cosine top\-60, BM25 top\-20, supersession/expiry/retraction filters, and category\-dependent blended scoring \(decay rateλc\\lambda\_\{c\}, blending weightαc\\alpha\_\{c\}, semantic floor\); category\-forced retrieval, multi\-hop entity expansion, and LLM distillation are omitted as they require external API calls\.RateMean Jaccard\(±\\pmstd\)Mean Displaced\(±\\pmstd\)Mean Kendallτ\\tau\(±\\pmstd\)0%1\.0001\.000\(±0\.000\\pm 0\.000\)0\.000\.00\(±0\.00\\pm 0\.00\)1\.0001\.000\(±0\.000\\pm 0\.000\)5%0\.9860\.986\(±0\.001\\pm 0\.001\)0\.150\.15\(±0\.01\\pm 0\.01\)0\.9920\.992\(±0\.001\\pm 0\.001\)10%0\.9740\.974\(±0\.002\\pm 0\.002\)0\.290\.29\(±0\.02\\pm 0\.02\)0\.9740\.974\(±0\.001\\pm 0\.001\)20%0\.9530\.953\(±0\.003\\pm 0\.003\)0\.540\.54\(±0\.03\\pm 0\.03\)0\.9550\.955\(±0\.002\\pm 0\.002\)30%0\.9280\.928\(±0\.001\\pm 0\.001\)0\.830\.83\(±0\.01\\pm 0\.01\)0\.9310\.931\(±0\.007\\pm 0\.007\)50%0\.9050\.905\(±0\.003\\pm 0\.003\)1\.111\.11\(±0\.04\\pm 0\.04\)0\.8970\.897\(±0\.007\\pm 0\.007\)Setup\.Across the 40 persona banks, 6,180 of 12,968 active entries \(47\.7%\) sit in the four confused categories and are therefore eligible to flip\. Flip counts are reported over*affected edge\-instances*rather than unique entries: the 6,180 eligible entries occupy8,9138\{,\}913edge\-instances across the banks, so at a 10% rate≈910\\approx 910instances are flipped per seed and at 50%,≈4,400\\approx 4\{,\}400\. \(Ten percent of the 6,180*unique*entries would be 618; the submitted version did not state which denominator the counts used\.\) When a label flips, the entry inherits*every*parameter of its new category—decay rateλc\\lambda\_\{c\}, blending weightαc\\alpha\_\{c\}, semantic floor, and numeric\-preservation behavior—so the reported stability reflects the full lifecycle\-policy effect of the swap, not a partial substitution\. Raw per\-seed numbers and pool statistics are released atperturbation\_study\_results\.json\.

### B\.2Ontology\-Aware Session Initialization \(Warm Start Protocol\)

Three session modes:Cold: low\-complexity intent; graph traversal skipped\.Warm: user declares intent; targeted traversal primes the session with the active frontier—the subgraph with highest recent activation in the relevant category neighborhood\.Evolving: starts warm, but conversation drifts; the system maintains a rolling query category vector \(exponential moving average\) and compares via cosine distance; when distance exceeds thresholdδ\\deltaforNNconsecutive turns, background traversal expands session context asynchronously\.

### B\.3Per\-User Parameter Evolution

The 10\+1 categories and base decay rates represent a population\-level default\. The architecture is designed to support per\-user parameter adaptation without LLM calls: a user who mentions hobbies frequently→\\toHobbies decay rate decreases; a user who changes preferences rapidly→\\toPreferences decay rate increases\. Parameter adaptation would use clean statistical signals: access frequency, temporal gap statistics, supersession rates per category\. We scope empirical validation of the adaptation loop to future deployment work\.

### B\.4Interpretability and User Control

Because every fact carries a human\-readable category label and a transparent lifecycle policy, the entire memory system becomes inspectable, auditable, and modifiable\. Users can view their memory by category, understand why facts persist or fade, correct misclassifications, and adjust retention\. Developers can debug retrieval failures with clear causal chains and structure downstream LLM context by category:

```
CORE IDENTITY (always relevant):
  - User has ADHD
  - User is a software engineer
CURRENT CONTEXT (time-sensitive):
  - Meeting at 3pm today
PREFERENCES (apply when relevant):
  - Prefers concise responses
```

### B\.5Safety and Robustness

Prompt injection via memory\.The ingestion classifier detects instructional content and quarantines it\. High\-sensitivity categories \(Health, Financial\) flag facts for reconfirmation if inconsistent with established patterns\.Confidence degradation\.Low\-confidence supersessions surface both facts with ambiguity noted\.Selective forgetting\.Deletion requests provide clean, verifiable removal with audit trail\.

### B\.6Emotional State as Signal

Transient emotional state \(“I’m frustrated right now”\) is deliberately excluded as a category\. Mood is a signal that modulates other categories: a message expressing frustration about a work deadline belongs in Obligations with an emotional loading modifier, not in a separate “Emotions” bucket\. Emotional loading detected at ingestion temporarily boosts the activation of the relevant category, with the boost itself subject to fast decay\.

## Appendix CLifecycleBench: Extended Methodology

Table 12:LifecycleBench attack vectors, referenced from §efsec:benchmark\. Each targets a distinct lifecycle failure mode;nnis the question count\.AVNameTestsnnAV1Superseded PreferenceReturn the*current*preference after an explicit change?75AV2Expired LogisticsRecognize that a past event is no longer active?75AV3Stable IdentityRetrieve identity facts buried under months of conversation?94AV4Multi\-Version FactReturn the latest version when a fact changed multiple times?44AV5Broad AggregationAggregate across multiple edges \(“all of X’s hobbies”\)?40AV6Cross\-Session ContradictionResolve contradictions between sessions?45AV7Selective ForgettingSuppress an explicitly retracted statement?40AV8Numeric PreservationReturn specific numbers \($950/month, 7 bass\)?63AV9Soft SupersessionHandle partial updates \(“thinking about” vs “committed to”\)?40Total516

### C\.1Persona Design

Each persona is a fully specified temporal state machine with explicit ground\-truth facts, session numbers, supersession chains, expiry dates, retractions with required language, and soft ambiguity\. Conversations are generated conversation\-first using Claude Opus 4\.6 with extended thinking under strict rules ensuring that facts emerge naturally through dialogue, the assistant has zero cross\-session memory, retractions are explicit, and contradictions are implicit\. Each persona spans 35 sessions across 18 simulated months with interleaved noise sessions\.

Diversity\.40 personas span 14 nationalities, ages 22–68, occupations from electrician to hospice chaplain\. This diversity is adversarial by design: learned memory policies must generalize across this combinatorial space, while ontology\-driven policies are distribution\-invariant\.

### C\.2On Synthetic Generation

LifecycleBench conversations are synthetically generated—as are those of every major memory benchmark in the literature\. LongMemEval\[[1](https://arxiv.org/html/2609.10413#bib.bib1)\]generates its multi\-session conversations with GPT\-4; LoCoMo\[[13](https://arxiv.org/html/2609.10413#bib.bib13)\]constructs dialogues synthetically and validates with human annotation; no published benchmark uses naturally occurring multi\-session personal conversations, because such data cannot be collected at scale without prohibitive privacy and IRB constraints\. The relevant question is therefore not*whether*a benchmark is synthetic, but whether its synthetic design enables*controlled evaluation*of the target phenomenon\. LifecycleBench’s contribution is precisely this control: each persona is a fully specified temporal state machine with explicit ground\-truth supersession chains, expiry dates, and retraction events, enabling the first benchmark where the correct answer depends on lifecycle state management rather than retrieval recall alone\. No naturalistic dataset can provide this because ground\-truth temporal state—which fact superseded which, when an obligation expired, what language the user used to retract—is unobservable without the controlled design\.

### C\.3Persona Examples

Table[13](https://arxiv.org/html/2609.10413#A3.T13)shows five LifecycleBench personas with representative lifecycle events\. Each persona spans∼\{\\sim\}35 sessions over 18 simulated months; only selected events are listed\. The five span ages2222–6161, three nationalities/heritages on three continents, and occupations from student\-barista to traditional barber to Inuvialuit wildlife researcher\. Quoted text is taken verbatim from the persona ground\-truth YAML files; session indices are noted as \(s\.nn\)\. The personas are fully synthetic, so no privacy concerns arise from the quotations\.

Table 13:Five LifecycleBench personas illustrating attack\-vector coverage\. Across these five rows the table illustrates AV1 \(superseded preference\), AV2 \(expired/upcoming logistics\), AV4 \(multi\-version fact\), AV7 \(retraction\), and AV9 \(soft/ambiguous supersession\)\.PersonaProfileAVLifecycle eventPriya Sharma34, ML engineer, Tamil\-American \(Austin, TX\)AV4Employer: “Works at Google on the Gemini memory team” \(s\. 1\)→\\to“Left Google, joining Anthropic” \(s\. 18\)\.AV1Diet: “vegetarian for like 5 years” \(s\. 3\)→\\to“started eating fish again … doctor said I needed more omega\-3s for the migraines” \(s\. 22\)\.AV7Pet plan: “looking at golden retriever puppies” \(s\. 12\)→\\to“the dog thing is dead\. Landlord said absolutely no pets” \(s\. 16\)\.Mehmet Yılmaz56, traditional barber, Turkish \(Kadıköy, Istanbul\)AV4Apprentice: “Burak has been with me 3 years” \(s\. 3\)→\\to“Burak opened his own place … now I have Deniz, 17 years old” \(s\. 20\)\.AV2Upcoming: “the guild meeting is September 12 \[2026\] … I am on the committee this year” \(s\. 29\); two earlier obligations \(hygiene inspection Feb 20 2025, wife’s cataract surgery Jun 3 2025\) must*not*surface as upcoming\.AV9Soft \(ambiguous\): “maybe 50–80 lira extra per service … I am thinking about it … not decided yet” \(s\. 27\); should not be reported as a definite menu change\.Lily Chen22, environmental science student \+ barista, Chinese\-Australian \(Melbourne\)AV4Partner: “me and soph have been together like 8 months” \(s\. 5\)→\\to“me and soph ended a while back\. i’m seeing someone now though, mika” \(s\. 22\)\.AV1Oat milk: “minor figures … the only one i trust for flat whites” \(s\. 6\)→\\to“minor figures changed their formula and its genuinely trash now … switched to bonsoy oat” \(s\. 25\)\.AV7Exchange: “i’m applying for exchange at ubc in vancouver\!\!” \(s\. 12\)→\\to“the ubc thing is dead … scrapping it\. forget i mentioned it” \(s\. 17\)\.Billy Kootook49, wildlife researcher & hunting guide, Inuvialuit \(Tuktoyaktuk, NWT\)AV1Tours: “polar bear tours … $2,400 a head” \(s\. 7\)→\\to“stopped the bear tours\. doing youth trips now … kids from other communities” \(s\. 26\)\.AV2Upcoming: “aerial survey June 4 \[2026\] for the muskox count\. helicopter out of Inuvik” \(s\. 28\)\.AV7Camp: “thinking about building a camp out at Husky Lakes” \(s\. 8\)→\\to“the Husky Lakes camp is dead\. the ground is thawing too fast … slumped 2 metres since last summer” \(s\. 16\)\.Diane Holloway61, hospice chaplain, American \(Asheville, NC\)AV1Hobby: “Perennials mostly — echinacea, black\-eyed Susan, butterfly weed” \(s\. 6\)→\\to“I’ve had to give up the garden … I’ve found watercolor … I paint the flowers I can no longer kneel beside” \(s\. 24\)\.AV4Denomination: “I was ordained Episcopal” \(s\. 3\)→\\to“I’ve moved to the UCC\. It was a long discernment” \(s\. 28\)\.AV7Book: “working on a book proposal … about chaplaincy, about how we sit with grief” \(s\. 11\)→\\to“the stories I would tell are not mine\. They belong to the families … The book is finished before it began” \(s\. 20\)\.

### C\.4Scale and Coverage

Table 14:LifecycleBench scale relative to LongMemEval\.MetricLongMemEval\-SLifecycleBenchRatioQuestions5005161\.0×1\.0\\timesPersonas / subjects1 \(implicit\)4040×40\\timesSessions per subject∼\{\\sim\}48 \(haystack\)350\.7×0\.7\\timesLifecycle\-relevant questions78 \(16%\)516 \(100%\)6\.6×6\.6\\timesCorpus statistics\.The 40 persona banks contain18,93618\{,\}936total entries \(12,96812\{,\}968active,5,9685\{,\}968inactive\)\. Of inactive entries,5,7805\{,\}780were deactivated by supersession,1313by explicit retraction, and175175are otherwise unclassified\. Across12,46012\{,\}460distinct slot keys,18\.6%18\.6\\%have been updated at least once \(chain length\>1\>1\); the longest chains reach4545–6565versions for high\-churn attributes \(e\.g\., evolving hobbies, current city, work schedule, family relationships\)\. Each persona spans exactly3535sessions over a mean of17\.417\.4simulated months \(range14\.9514\.95–18\.5318\.53\), at14\.514\.5–36\.936\.9entries per month\. The OTHER category accounts for0\.12%0\.12\\%of entries \(1616of12,96812\{,\}968\), confirming that the 10\-category coverage is near\-exhaustive\. The three most frequent categories are Projects & Endeavors \(20\.7%20\.7\\%\), Relational Bonds \(16\.9%16\.9\\%\), and Obligations \(14\.2%14\.2\\%\)\.

### C\.5Evaluation Metrics

\(1\) AV\-specific pass rate: does the top\-KKretrieval set support the correct answer? \(2\) Staleness penalty: does it contain outdated edges? An LLM judge \(Claude Sonnet\) evaluates each \(question, edge\) pair\. Top\-10 judge window \(split: correct\-answer in top\-10, staleness in top\-5\)\.

Generator\-judge independence\.LifecycleBench conversations are generated by Claude Opus 4\.6 with extended thinking, while the retrieval and E2E judges use Claude Sonnet\. Although both are Anthropic models, the judge evaluates factual correctness against structured ground\-truth YAML \(supersession chains, expiry dates, retraction events\), not generation quality\. The judge’s task is to determine whether a specific factual answer matches the YAML specification; model\-family affinity does not advantage or disadvantage any memory system, since all five systems are evaluated by the same judge on the same questions\. Cross\-generator validation on Kimi K2\.5 \(Moonshot, open\-weight; Appendix[AB](https://arxiv.org/html/2609.10413#A28)\) preserves the confabulation hierarchy exactly, providing evidence that the ranking is judge\-invariant\.

Why not MRR?Replication of Liu et al\.\[[15](https://arxiv.org/html/2609.10413#bib.bib15)\]on Claude Sonnet \(2026\) at 50\-document scale shows no significant positional effect \(r=−0\.009r=\-0\.009,p=0\.65p=0\.65\)\. The model processes all retrieved facts with near\-equal attention\. MRR is therefore uninformative for downstream accuracy\. The positional staleness effect operates through conflict resolution under contradiction, not utilization failure\. We nevertheless report MRR in Appendix[D](https://arxiv.org/html/2609.10413#A4)for comparability with prior work \(Zep/Graphiti and Memory\-R1 report MRR as a primary metric\), while using pass rate as our primary evaluation metric throughout\.

Configurations\.Four configs as a2×22\\times 2ablation: decay type \(behavioral vs uniform\)×\\timesrouting \(on/off\)\. Category\-specificα\\alpharanges from 0\.05 \(Financial\) to 0\.40 \(Logistical\)\.

### C\.6Benchmark Independence Analysis

A natural concern with any co\-introduced benchmark is whether the evaluation instrument favors the co\-introduced system\. We address this along four axes\.

Exhaustive failure\-mode coverage\.The 9 attack vectors enumerate the exhaustive set of temporal\-state failure modes for persistent personal memory rather than FR\-specific capabilities\. A fact can be replaced \(AV1, AV4\), an event can expire \(AV2\), a statement can be retracted \(AV7\), information can be partially updated \(AV9\), stable facts can be buried under conversation volume \(AV3\), facts can require cross\-edge aggregation \(AV5\), sessions can contradict each other \(AV6\), and specific numeric values can be lost in abstraction \(AV8\)\. Any independently constructed lifecycle benchmark would need to cover the same failure modes, because these are properties of the problem domain, not of any particular solution\.

FR does not dominate all vectors\.MemoryOS leads AV6 \(Cross\-Session Contradiction\) at73%73\\%versus FR\-Bank’s64%64\\%, and leads AV7 on the retrieval metric\. FR\-Graphiti, not FR\-Bank, leads AV2 and AV8\. FR\-Bank achieves only5%5\\%retrieval pass on AV7 \(Selective Forgetting\) and near\-zero correct rates on AV5 and AV6 end\-to\-end \(Table[42](https://arxiv.org/html/2609.10413#A14.T42)\)\. If the benchmark were designed to favor FR, these gaps would not exist\. \(The submitted version stated that Memory\-R1 leads AV3 at94%94\\%; that comparison was against FR\-Graphiti’s78%78\\%\. FR\-Bank leads AV3 at97%97\\%, and Memory\-R1 leads no attack vector\.\)

Cross\-benchmark validation\.Cross\-validation on LongMemEval\-S—an independently constructed benchmark predating this work—confirms that FR’s gains concentrate where lifecycle mechanisms apply\. Lifecycle is aggregate\-neutral on the 317\-question matched subset \(\+2\.2\+2\.2pp net; §[D\.2](https://arxiv.org/html/2609.10413#A4.SS2)\) and approximately neutral on the question categories where temporal\-state management does not apply\. Where lifecycle correctly removes facts that LongMemEval still considers retrievable—knowledge\-update \(−6\.4\-6\.4pp\) and single\-session\-user—the cost reflects a benchmark criterion limitation rather than a system regression: the Wu et al\. judge marks responses correct when stale facts are present alongside the updated answer\.

Ontology discrimination\.The ontology ablation \(Table[4](https://arxiv.org/html/2609.10413#A1.T4)\) demonstrates that LifecycleBench discriminates between ontology approaches: the behavioral partition outperforms the cognitive partition on 7 of 9 attack vectors under the same pipeline, confirming that the benchmark tests ontology quality rather than system identity\.

We acknowledge that co\-design risk cannot be fully eliminated without independent replication\. We release LifecycleBench \(personas, conversations, questions, ground truth, evaluation code\) to enable the community to evaluate alternative approaches under identical conditions\.

## Appendix DExtended Experimental Results

### D\.1LongMemEval Detailed Results

##### Primary result: LongMemEval\-S 500\-question canonical benchmark\.

The full 500\-question LongMemEval\-S setup of Wu et al\. \(ICLR 2025\) is our headline evaluation\. We rerun the full suite 10 times under identical configuration \(temperature 0 throughout, same retrieval pipeline and top\-10 facts per question\) to characterize judge non\-determinism\. All 10 runs land at or above the locked baseline of 74\.2%, with a mean of 75\.2% and a maximum of 76\.6% \(Table[15](https://arxiv.org/html/2609.10413#A4.T15)\)\. Per\-category dispersion is small except for single\-session\-preference, where the small denominator \(n=30n\{=\}30\) inflates stdev\.

Table 15:LongMemEval\-S 500\-question variance over 10 identical reruns \(temperature 0, identical configuration\)\. “stdev” is sample standard deviation in percentage points\.Categorynnminmeanmedianmaxstdevknowledge\-update7880\.8%82\.4%82\.1%84\.6%1\.49multi\-session13363\.9%65\.9%65\.8%68\.4%1\.38single\-session\-assistant5671\.4%75\.4%75\.9%78\.6%2\.64single\-session\-preference3053\.3%64\.3%65\.0%70\.0%5\.45single\-session\-user7091\.4%92\.7%92\.9%92\.9%0\.45temporal\-reasoning13371\.4%73\.5%73\.7%75\.9%1\.32TOTAL50074\.4%75\.2%75\.1%76\.6%0\.70
##### Peer\-reviewed comparison on LongMemEval\-S\.

Table[16](https://arxiv.org/html/2609.10413#A4.T16)places 75\.2% alongside the two prior peer\-reviewed LongMemEval reports\. Industry numbers \(Zep, Mem0, MemoryOS\) are not peer\-reviewed and do not disclose enough protocol detail for a like\-for\-like comparison; see Appendix[AA](https://arxiv.org/html/2609.10413#A27)for the judge protocol we follow\.

Table 16:Peer\-reviewed LongMemEval\-S results prior to and including this work\.SystemVenuePassJudge / protocolFR\-Bank \(this work\)NeurIPS submission75\.2%gpt\-4o\-2024\-08\-06, 5\-template Wu et al\. rubricRMM\[[3](https://arxiv.org/html/2609.10413#bib.bib3)\]ACL 202570\.4%Gemini\-1\.5\-Pro judge, single generic promptWu et al\. baselinesICLR 202555–60%gpt\-4o\-2024\-08\-06, 5\-template \(full context\)
##### Secondary: 234\-question oracle POC subset\.

As an earlier proof\-of\-concept we evaluated on the 234\-question oracle subset used by Zep/Graphiti\. Table[17](https://arxiv.org/html/2609.10413#A4.T17)reports those numbers; they were produced with an earlier FR\-Bank configuration and are retained here only as context for the \+8\.3pp gain over the Zep/Graphiti arXiv report\. The per\-type breakdown in Table[18](https://arxiv.org/html/2609.10413#A4.T18)reflects that same earlier configuration; the single\-session\-assistant category has since moved from 50\.0% on the POC subset to 75\.4% mean on the full LongMemEval\-S \(Table[15](https://arxiv.org/html/2609.10413#A4.T15)\) after the fixes described in Appendix[AA](https://arxiv.org/html/2609.10413#A27)\.

Table 17:LongMemEval results on the 234\-question oracle POC subset \(earlier FR\-Bank configuration\)\. Primary LongMemEval\-S numbers are in Table[15](https://arxiv.org/html/2609.10413#A4.T15)\.SystemPass@10MRRSourceFR\-Bank79\.5%0\.668This workZep/Graphiti71\.2%—\[[2](https://arxiv.org/html/2609.10413#bib.bib2)\]\(arXiv\)FR\-Graphiti \(behavioral\)32\.1%0\.232This work \(decay only\)FR\-Graphiti \(uniform\)32\.1%0\.231This work \(decay only\)FR\-Graphiti \(cognitive\)32\.1%0\.231This work \(decay only\)Table 18:FR\-Bank per\-question\-type results on the 234\-question oracle POC subset \(earlier configuration\)\.Question TypeCountPass@10MRRsingle\-session\-preference3093\.3%0\.736single\-session\-user7088\.6%0\.800knowledge\-update7887\.2%0\.756single\-session\-assistant5650\.0%0\.342Zero retrieval cost on LongMemEval\.On the Graphiti\-based evaluation \(16,138 edges\), no decay engine achieves significant advantage after Bonferroni correction\. All effect sizes are negligible \(\|d\|<0\.19\|d\|<0\.19\)\. Behavioral lifecycle policies impose zero measurable retrieval cost\.

### D\.2Lifecycle Contribution Decomposition

Table 19:LongMemEval lifecycle ablation\. Retrieval pipeline: \+7\.4pp; lifecycle: \+0\.9pp net\.ConfigurationPass@10MRRFR\-Bank \(retrieval \+ lifecycle\)79\.5%0\.668FR\-Bank \(retrieval only, no lifecycle\)78\.6%0\.644Zep/Graphiti \(peer\-reviewed\)71\.2%—Table 20:Per\-question\-type lifecycle decomposition on the234\-question oracle POC subset\. Lifecycle and no\-lifecycle arms were evaluated on identical banks; cross\-pipeline LME\-S comparisons \(with\-lifecycle pipeline vs\. no\-lifecycle oracle pipeline\) are not used here because they involve different judge models and ingestion paths\. The knowledge\-update row of the submitted version reported87\.2%87\.2\\%vs\.80\.8%80\.8\\%\(\+6\.4\+6\.4pp\); those cells trace to no surviving artifact and are withdrawn here\. The artifact\-backed knowledge\-update decomposition is on the 317\-question matched subset \(Table[21](https://arxiv.org/html/2609.10413#A4.T21)\), where the effect is−6\.4\-6\.4pp\. This table and Table[21](https://arxiv.org/html/2609.10413#A4.T21)are two different subsets and must not be read as one series\.Question TypeWith LCNo LCDeltaInterpretationknowledge\-update*withdrawn*See Table[21](https://arxiv.org/html/2609.10413#A4.T21)single\-session\-assistant51\.8%50\.0%\+1\.8ppMarginal benefitsingle\-session\-preference93\.3%93\.3%\+0\.0ppNo effectsingle\-session\-user87\.1%92\.9%−\-5\.8ppSupersession removes some factsOverall79\.5%78\.6%\+0\.9ppNet neutral on mixed question setTable 21:Artifact\-backed lifecycle decomposition on the317\-question matched subsetof LongMemEval\-S \(the questions for which both configurations were evaluated on identical banks\)\. The knowledge\-update effect is negative: the Wu et al\. judge credits a response when the superseded fact is present alongside the updated one, so lifecycle filtering is penalized for producing cleaner context \(§[D\.2](https://arxiv.org/html/2609.10413#A4.SS2)\)\.Question TypeWith LCNo LCDeltaInterpretationknowledge\-update79\.5%85\.9%−\-6\.4ppJudge\-criterion artifact, not a regressionsingle\-session\-user——−\-2\.9ppNegligibletemporal\-reasoning——\+0\.0ppNo effectOverall75\.1%72\.9%\+2\.2ppAggregate\-neutral to mildly positive##### LME\-S lifecycle decomposition \(317\-question matched subset\)\.

On the 317 LongMemEval\-S questions for which both lifecycle and no\-lifecycle configurations were evaluated on identical banks, lifecycle contributes\+2\.2\+2\.2pp net \(72\.9%→75\.1%72\.9\\%\\to 75\.1\\%\)\. The contribution concentrates on the question categories where temporal\-state management is required: knowledge\-update and multi\-session questions, where the lifecycle layer removes contradictory or superseded facts before retrieval; on the remaining task types lifecycle is approximately neutral\. The knowledge\-update inversion \(−6\.4\-6\.4pp\) reveals a benchmark criterion limitation: the Wu et al\. judge marks responses correct when both the old and updated answer are present, so lifecycle filtering that correctly removes superseded facts is penalized for producing cleaner context\. This criterion implicitly treats stale facts as harmless—an assumption directly contradicted by our end\-to\-end evaluation, where stale retrieval context produces 72–78% confabulation \(Table[40](https://arxiv.org/html/2609.10413#A14.T40)\)\. The remaining task types \(single\-session\-user, temporal\-reasoning\) show negligible difference \(−2\.9\-2\.9pp,\+0\.0\+0\.0pp\), confirming that lifecycle imposes zero cost where it does not apply\.

The near\-neutral net contribution on both subsets masks a consistent pattern: the losses sit exactly where lifecycle filtering correctly removes facts that LongMemEval still considers retrievable—knowledge\-update \(−6\.4\-6\.4pp on the 317\-matched subset\) and single\-session\-user \(−5\.8\-5\.8pp on the POC subset\)\. LongMemEval’s question distribution also limits lifecycle opportunity: only 33% of questions involve temporal state transitions\.

### D\.3Scaling Validation

Table[22](https://arxiv.org/html/2609.10413#A4.T22)presents five\-phase scaling validation from 8 to 40 personas, confirming that lifecycle gains widen with scale while staleness remains stable\.

Table 22:Five\-phase scaling validation\.MetricPh\. 2 \(8p\)Ph\. 3 \(20p\)Ph\. 5b \(40p\)Ph\. 5c \(40p\)TrendFull pass rate63%66%71%73%\+10pp totalFull staleness4%6%7%8%StableBaseline pass rate62%55%59%61%StableBehavioralΔ\\Deltapass\+1pp\+11pp\+12pp\+12ppWidening

### D\.4Substrate Independence

Table 23:Substrate comparison: same lifecycle policies on two infrastructures\.SystemPassStaleMRRHit@5FR\-Graphiti73%8%0\.47875%FR\-Bank76\.9%15\.5%0\.83097\.0%The lifecycle layer transfers without modification, confirming it is a policy contribution, not an infrastructure artifact\. FR\-Graphiti retains a staleness advantage \(8% vs 15\.5%\) due to graph\-based supersession tracking, while FR\-Bank’s enhanced retrieval \(BM25 \+ distillation\) compensates for the absence of graph traversal\.

### D\.5Infrastructure Findings

World\-knowledge contamination\.86% of extracted edges were world knowledge—reduced to 1\.4% with detection filtering across∼\{\\sim\}12,700 edges\.

Numeric preservation\.Graphiti’s deduplication pipeline systematically loses numeric values through dedup resolution and bulk dedup canonical selection\. Numeric\-preference resolution increased numeric edge density from∼\{\\sim\}5% to 20\.1%\.

Per\-source score normalization\.Prior to normalization, 99\.1% of top\-5 results came from Graphiti’s semantic search alone\. After per\-source normalization, all retrieval strategies became meaningful contributors\.

### D\.6Bootstrap Confidence Intervals and Pairwise Significance

To quantify the statistical resolution of the cross\-system comparison and the FR\-Graphiti ablation we compute paired bootstrap 95% confidence intervals \(10,000 resamples, seed=42\) and McNemar’s exact test on the per\-question paired binary outcomes \(n=516n=516\)\.

Table 24:LifecycleBench pass rates with95%95\\%paired bootstrap confidence intervals \(10,000 resamples, seed=42,n=516n=516\)\. Pairwise significance vs FR\-Bank via McNemar’s exact test on paired binary outcomes\. The FR\-Bank vs FR\-Graphiti gap is not statistically significant \(p=0\.10p=0\.10\); two implementations of the same lifecycle policy land within statistical resolution of each other\.SystemPass Rate95% CIMcNemarppvs FR\-BankFR\-Bank76\.9%76\.9\\%\[73\.3,80\.6\]\[73\.3,80\.6\]—FR\-Graphiti72\.9%72\.9\\%\[69\.0,76\.6\]\[69\.0,76\.6\]0\.100\.10MemoryOS70\.5%70\.5\\%\[66\.5,74\.4\]\[66\.5,74\.4\]0\.018∗0\.018^\{\*\}Memory\-R166\.9%66\.9\\%\[62\.8,70\.9\]\[62\.8,70\.9\]<0\.001∗∗∗<\\\!0\.001^\{\*\*\*\}Mem060\.9%60\.9\\%\[56\.6,65\.1\]\[56\.6,65\.1\]<0\.001∗∗∗<\\\!0\.001^\{\*\*\*\}FR\-Graphiti ablation significance\.Paired bootstrap on the four ablation arms \(full,−\-routing,−\-behavioral decay, baseline;n=516n=516\): full vs\. baselineΔ=\+12\.2\\Delta=\+12\.2pp,95%95\\%CI\[8\.3,16\.1\]\[8\.3,16\.1\], McNemarp<0\.001p<0\.001; full vs\. no\-routingΔ=\+6\.2\\Delta=\+6\.2pp\[2\.9,9\.7\]\[2\.9,9\.7\]; full vs\. uniform decayΔ=\+6\.4\\Delta=\+6\.4pp\[3\.5,9\.3\]\[3\.5,9\.3\]\(full72\.9%72\.9\\%, no\-routing66\.7%66\.7\\%, uniform decay66\.5%66\.5\\%, baseline60\.7%60\.7\\%\)\. Each ablation step removes a statistically significant share of the lifecycle gain\. The signs of these three deltas were inverted in the submitted version; the per\-AV gains in Table[25](https://arxiv.org/html/2609.10413#A4.T25)were already positive \(Appendix[AI](https://arxiv.org/html/2609.10413#A35)\)\.

### D\.7Cross\-System Per\-AV Comparison

Table[25](https://arxiv.org/html/2609.10413#A4.T25)reports per\-attack\-vector results for FR\-Graphiti \(full vs\. baseline\)\. The largest gains appear precisely where lifecycle management applies:\+21\+21pp on superseded preferences \(AV1\),\+20\+20pp on expired logistics \(AV2\),\+22\+22pp on multi\-version facts \(AV4\), and\+10\+10pp on selective forgetting \(AV7\)\. Table[26](https://arxiv.org/html/2609.10413#A4.T26)presents the full five\-system per\-attack\-vector comparison\. FR\-Bank leads AV1, AV3, AV4 and AV5 outright, plus a three\-way tie on AV9; the remaining vectors are led by systems with complementary strengths \(FR\-Graphiti on AV2 and AV8, MemoryOS on AV6 and AV7\)\. Memory\-R1 leads no attack vector\.

Table 25:Per\-attack\-vector results on FR\-Graphiti \(full vs\. baseline\)\.Attack VectornnFull PassFull StaleBase PassBase StaleΔ\\DeltaPassAV1 Superseded Preference7561%13%40%27%\+21ppAV2 Expired Logistics7593%7%73%24%\+20ppAV3 Stable Identity9478%0%66%0%\+12ppAV4 Multi\-Version Fact4461%20%39%43%\+22ppAV5 Broad Aggregation4090%2%82%0%\+8ppAV6 Cross\-Session4540%20%36%36%\+4ppAV7 Selective Forgetting4040%12%30%32%\+10ppAV8 Numeric Preservation6394%5%94%8%0ppAV9 Soft Supersession4078%0%72%2%\+6ppOverall51673%8%61%18%\+12pp

Table 26:Per\-AV cross\-system comparison \(five systems\)\.Attack VectornnFR\-B PassFR\-B StaleFR\-G PassFR\-G StaleMR1 PassMR1 StaleMem0 PassMem0 StaleMOS PassMOS StaleAV1 Superseded Pref\.7567%28%61%13%64%17%44%49%60%16%AV2 Expired Logistics7588%7%93%7%75%25%65%33%88%9%AV3 Stable Identity9497%0%78%0%94%1%87%0%79%0%AV4 Multi\-Version4486%14%61%20%66%18%45%39%64%11%AV5 Broad Query4098%2%90%2%98%7%88%3%95%2%AV6 Cross\-Session4564%31%40%20%40%24%44%47%73%2%AV7 Selective Forgetting405%60%40%12%15%42%5%80%57%22%AV8 Numeric Preserv\.6384%6%94%5%57%2%67%8%44%0%AV9 Soft Supersession4078%10%78%0%62%15%78%3%72%2%Overall51676\.9%15\.5%73%8%66\.9%15\.3%61%27%70\.5%7%

### D\.8Efficiency and Positional Staleness

Table[27](https://arxiv.org/html/2609.10413#A4.T27)summarizes context efficiency metrics\. FR achieves3×3\\timeslower stale token rate and8×8\\timeslower rate of stale facts at rank 1 compared to Mem0\.

Table 27:Context efficiency and positional staleness\.MetricFRMem0RatioSignal:noise ratio85%67%1\.3×1\.3\\timesStale token rate3%9%3×3\\timesStale cost/1M queries$13$382\.9×2\.9\\timesStale fact at rank 12\.1%16\.5%8×8\\timesPositional stale exposure14%37%2\.6×2\.6\\timesWeighted staleness risk0\.511\.843\.6×3\.6\\times
### D\.9Deterministic Lifecycle Layer Latency

We profile the deterministic lifecycle layer—Sections 5–7 of the retrieval pipeline inlifecycle\_bank\.py—in isolation from all non\-deterministic work\. The measured region covers: supersession by slot\-key grouping, event\-time expiry, retraction masking, harmonic\-mean decay over soft category weights, anticipatory activation, blended scoring, semantic and numeric preservation floors, and top\-NNselection by blended score\. Excluded from the timed region: embedding, cosine search, BM25, category\-forced retrieval, multi\-hop entity expansion, the one LLM distillation call, and disk I/O\. The 40 LifecycleBench persona banks \(total18,93618\{,\}936entries,12,96812\{,\}968active\) are loaded once outside the timing loop\. Each persona contributes a pool of sizekkbuilt from a deterministic random sample of its active entries with simulated post\-distillation similarity scores drawn from\[0\.70,0\.99\]\[0\.70,0\.99\]\. Measured branches fire at realistic rates:98\.8%98\.8\\%of entries carry a slot key \(supersession\),95\.8%95\.8\\%multi\-category \(harmonic\-mean decay is non\-degenerate\),10\.1%10\.1\\%event\-time\-anchored,27\.3%27\.3\\%numeric\-preservation candidates, and0\.2%0\.2\\%retracted\.

Table 28:Deterministic lifecycle layer latency on the 40 LifecycleBench persona banks\. Primary row \(k=20k\{=\}20\): 1,000 iterations per persona, 50\-iteration warmup\. Scaling rows: 1,000 iterations over akk\-sized pool sampled across personas \(with synthetic id rewrites to avoid cross\-bank id collisions\)\. Single\-threaded Python 3\.13 on AMD Zen 3\.Pool sizekkN trialsp50 \(ms\)p95 \(ms\)p99 \(ms\)mean \(ms\)2020\(primary, 40 personas\)40,00040\{,\}0000\.047\\mathbf\{0\.047\}0\.0530\.0530\.0850\.0850\.0480\.0482020\(scaling, pooled\)1,0001\{,\}0000\.0400\.0400\.0420\.0420\.0540\.0540\.0410\.04150501,0001\{,\}0000\.0920\.0920\.1030\.1030\.1590\.1590\.0950\.0951001001,0001\{,\}0000\.1860\.1860\.2400\.2400\.3410\.3410\.1940\.1942002001,0001\{,\}0000\.3790\.3790\.4130\.4130\.5100\.5100\.3850\.3855005001,0001\{,\}0000\.9800\.9801\.1261\.1261\.4731\.4731\.0031\.003100010001,0001\{,\}0001\.9581\.9582\.3022\.3022\.7622\.7622\.0102\.010Linearity is tight: thek=1000k\{=\}1000median is48\.5×48\.5\\timesthek=20k\{=\}20median versus the theoretical50×50\\times, and the per\-candidate slope is1\.96​μ​s1\.96\\,\\mu\\mathrm\{s\}\. Production workloads operate atk=20k=20, where the full deterministic layer costs𝟒𝟕​μ​𝐬\\mathbf\{47\\,\\mu s\}at the median—three orders of magnitude below the bounded LLM distillation call, and negligible against the cosine\-similarity work overnnstored edges\. The claim in §[4](https://arxiv.org/html/2609.10413#S4)that the lifecycle layer is a sub\-millisecond deterministic pipeline is confirmed empirically\.

### D\.10Controlled Comparison: 14 Event\-Time Cases

Cross\-system mechanism analysis on AV2 reveals 14 questions where FR’s expiry filter suppressed expired facts that Mem0 surfaced \(staleness=1\.0\)\. The same judge evaluated both systems on the same questions—identical inputs, opposite outcomes, determined solely by lifecycle filtering\.

Table 29:Controlled comparison: same question, same judge, opposite outcomes\.Expired FactFRMem0Mechanism“Greg’s birthday is this Saturday” \(past\)SuppressedStale=1\.0Date\-aware expiry filter“ACA exam 2025\-09\-03” \(expired 12 mo ago\)SuppressedStale=1\.0ISO date extraction“Demo scheduled for March” \(past\)SuppressedStale=1\.0Contextual month parsing“Flight at 6am tomorrow” \(long past\)SuppressedStale=1\.0Relative date resolution

### D\.11Failure Taxonomy

Automated classification of 90 failures at 20\-persona scale: Retrieval Miss 43 \(47\.8%\), Extraction Missing 25 \(27\.8%\), Stale Dominance 12 \(13\.3%\), Extraction Weak 7 \(7\.8%\), Cross\-Category 3 \(3\.3%\)\. AV7 failures are 100% extraction missing\. AV3 failures are 90% retrieval miss\.

### D\.12Reasoning Does Not Close the Architectural Gap

Table 30:Reasoning vs non\-reasoning\. The 18\.2pp architectural gap is unclosable by compute\.InterventionConfab\.Δ\\DeltaCostMem0 \+ no reasoning \(baseline\)45\.1%——Mem0 \+ reasoning40\.6%−\-4\.5pp\+11% tokensFR \+ no reasoning23\.9%−\-21\.2pp$0FR \+ reasoning22\.4%−\-22\.7pp\+11%Queries with stale facts consume \+9\.2 reasoning tokens on average \(\+11%\) as the model detects contradictions\.

### D\.13The Retrieval Metric Paradox

For AV7 questions where MemoryOS retrieval passes, 22/23 cases \(96%\) had hierarchical summarization replace specific retracted plans with generic summaries\. The judge marks these as passing because no stale fact is present—but no useful fact is present either\. End\-to\-end: MemoryOS 7\.5% correct on AV7 versus FR\-Bank’s 37\.5%\.

Table 31:Retrieval metric paradox on AV7\.MetricFR\-BankMemoryOSAV7 retrieval pass5%57%AV7 retrieval staleness60%22%AV7 E2E correct37\.5%7\.5%AV7 E2E confab22\.5%32\.5%AV7 E2E abstain32\.5%60\.0%

## Appendix EDetailed Gap Analysis Per System

Table 32:Gap analysis\. “Cog\.” = cognitive categories without behavioral conditioning\. Mem0 gaps empirically validated on LifecycleBench \(§[6](https://arxiv.org/html/2609.10413#S6)\)\.GapZepA\-MEMMemBankMem0MemGPTMemOSMem\-R1MIRIXFluxOursBehavioral ontology✗✗✗✗✗Hier\.a✗Cog\.✗✓Per\-category lifecycle✗✗Uniform✗✗✗✗✗✗✓Slot\-key supersessionBinary——✗✗✗✗✗—SoftEvent\-time validity✗✗✗✗✗✗✗✗✗✓Multi\-clock temporalBi\-temp\.✗Single✗✗✗✗✗✗3 clocksAnticipatory activation✗✗✗✗✗✗✗✗✗✓Category\-aware routing✗✗✗✗✗✗✗Partial✗✓Session initialization✗✗✗✗✗✗✗✗✗✓Emotional loading signal✗✗✗✗✗✗✗✗✗✓Deterministic lifecycle policyPartial✗Partial✗✗Partial✗✗Partial✓Interpretable policy————✗—✗——✓User\-modifiable policy✗✗✗✗✗✗✗✗✗✓

- aHier\. = hierarchical temporal tiers \(STM/MTM/LPM\) with persona/topic partitions, distinct from cognitive \(episodic/semantic/procedural\) typology\.

### E\.1Zep/Graphiti \(2025\): Eight Identified Gaps

Zep achieves 94\.8% on DMR and up to 71\.2% on LongMemEval\.Gap 1: No forgetting mechanism\.Facts either exist or get explicitly superseded\.Gap 2: No behavioral awareness\.Scheduling details and identity traits are structurally identical edges\.Gap 3: Purely reactive retrieval\.No anticipatory capability\.Gap 4: No session initialization intelligence\.Gap 5: Communities are structural, not behavioral\.Gap 6: Binary supersession under ambiguity\.Gap 7: Noisy retrieval on certain query types\.Gap 8: Self\-identified ontology gap\.

### E\.2MemoryBank \(AAAI 2024\): Five Gaps

Gap 1:Single uniform forgetting curve\.Gap 2:No graph structure\.Gap 3:Single temporal reference frame\.Gap 4:No behavioral categorization\.Gap 5:Limited evaluation\.

### E\.3A\-MEM \(NeurIPS 2025\): Four Gaps

Gap 1:No temporal dynamics\.Gap 2:No forgetting\.Gap 3:Content\-driven, not behavior\-driven evolution\.Gap 4:LLM\-heavy at runtime\.

### E\.4MemGPT / Letta \(2024\): Three Gaps

Gap 1:The LLM is the policy—expensive, opaque, and unreliable\.Gap 2:No internal structure in archival\.Gap 3:No temporal decay, supersession, or event\-time validity\.

### E\.5Mem0 \(2025\): Four Gaps \(Empirically Validated\)

Gap 1:No structured lifecycle\.*Validated: AV1 staleness is 49%\.*Gap 2:No category awareness\.*Validated: 87% on AV3 but 44% on AV1 and 5% on AV7\.*Gap 3:No event\-time expiry\.*Validated: AV2 staleness is 33%\.*Gap 4:Default storage does not persist between processes\.

### E\.6MemoryOS \(2025\): Three Gaps

Gap 1:Cognitive ontology, not behavioral\.*Validated: 70\.5% retrieval pass but 13\.2% E2E correct\.*Gap 2:No per\-category decay conditioning\.Gap 3:Fixed hierarchy with30×30\\timesingestion compute\.

### E\.7Memory\-R1 \(2025\): Four Gaps

Gap 1:Learned policy is opaque\.Gap 2:Requires massive interaction data\.Gap 3:No behavioral structure in action space\.Gap 4:No multi\-reference\-frame temporal sensitivity\.

### E\.8MIRIX \(2025\) and FluxMem \(2026\)

MIRIX: cognitive types; uniform temporal treatment; LLM\-heavy\.FluxMem: adapts structure not policy; orthogonal\.

### E\.9Architectural Prerequisites for Lifecycle Management

The systems compared in this paper were each designed for related but distinct goals: Mem0 prioritizes a clean operational interface over a vector store; Memory\-R1 trains an RL policy over an explicit operation vocabulary; MemoryOS optimizes hierarchical consolidation for retrieval throughput\. Lifecycle management—per\-fact event\-time validity, slot\-key supersession, and explicit retraction—was not a primary design objective for any of them\. A reasonable question is whether lifecycle behavior could be added to these systems as a metadata extension\. Based on a code\-level audit of each system’s evaluation harness and core library, we find that the gap is architectural rather than notational: each system has at least one load\-bearing structural decision that prevents lifecycle behavior from emerging even after metadata fields are added\.

##### Five prerequisites for lifecycle behavior\.

A retrieval system that supports lifecycle queries \(“what is current?” versus “what was previously the case?”\) requires:

1. 1\.per\-fact identity preserved through the ingestion pipeline;
2. 2\.per\-fact metadata that survives ingestion \(event\-time, slot\-key, lifecycle state\);
3. 3\.non\-overwrite update semantics that preserve the prior state when a new fact arrives;
4. 4\.a hook in the retrieval path where metadata can score or filter results;
5. 5\.query\-intent classification that selects the appropriate scoring or filter at query time\.

##### Feature compatibility\.

Table[33](https://arxiv.org/html/2609.10413#A5.T33)summarizes whether each lifecycle feature can be added to each competitor without architectural change\. We categorize each cell as*Moderate*\(new schema field with filter wrapper, retrieval path exists\),*Hard*\(new retrieval mechanism, RL retraining, or path fork\),*Impossible*\(requires rebuilding the core\), or≡\\equivFR \(adding the feature reimplements FR’s pipeline\)\.

Table 33:Lifecycle\-feature feasibility per system\.*Moderate*= new schema field plus filter wrapper;*Hard*= new retrieval mechanism / fork or RL retraining;*Impossible*= requires architectural rebuild;≡\\equivFR = adding the feature reimplements FR’s pipeline\.FeatureMem0Memory\-R1MemoryOSSlot\-key supersessionHardHardHardEvent\-time validityModerateHardModerateRetraction \(mark inactive\)ModerateHard†HardQuery\-conditioned state maskHardHardModerateCategory\-aware routingModerateHardModerateDifferential decay per categoryHardImpossible‡ModerateSoft supersession \(both kept\)HardHard≡\\equivFR
†Prompt edit is cheap, but\_\_slots\_\_cannot persist anis\_retractedflag without breaking persisted banks; the GRPO\-trained version requires retraining\.‡No decay function exists in the retrieval path; cosine is unweighted, and adding per\-category time\-decay would require modifying the reward signal of the trained policy\.

##### Mem0\.

The vector\-storeUPDATEoperation is a hard overwrite of the embedding and payload \(mem0/memory/main\.py:1142\-\-1194\); the prior embedding is not retained anywhere queryable, although a SQLite history row is written \(storage\.py:126\-\-150\)\. Custom metadata is passed through cleanly \(main\.py:401, 985\), and the search API supports pre\-ranking metadata filters \(main\.py:811\-\-815, 956\)\. The blocker is therefore not the metadata path but the*state\-preserving update path*: a deactivate\-and\-add semantics that retains both the prior and current entry under different lifecycle flags requires forking\_update\_memoryand\_search\_vector\_store\.

##### Memory\-R1\.

Two compounding fixed contracts\. First, the storage record is locked to four fields by\_\_slots\_\_ = \("id", "text", "timestamp", "source\_session"\)\(evaluate\_memoryr1\.py:100\-\-107\); addingslot\_key,event\_time, oris\_retractedis backward\-incompatible with persisted banks\. Second, the Manager’s action vocabulary is fixed as\{\\\{ADD,UPDATE,DELETE,NONE\}\\\}in the system prompt \(:294\-\-306\); in the GRPO\-trained version it is fixed in the trained policy, so adding aRETRACTaction requires re\-training with a new reward signal\. Even if both are addressed, the Answer Agent’s pure\-cosine retrieval \(:139\-\-148\) provides no scoring hook where a state mask could be applied—a third, independent fork point\.

##### MemoryOS\.

Per\-fact identity is preserved in STM \(short\_term\.py:16\-\-23\) and within MTM sessions, but the MTM→\\toLTM consolidation step \(memoryos\.py:162\-\-200\) extracts a monolithic profile string plus a flat knowledge deque \(long\_term\.py:17\-\-18\); neither carries back a link to the originating MTM page\. After consolidation, two contradictory LTM facts coexist with no mechanism for fact\-level invalidation \(long\_term\.py:69\-\-73\)\. Timestamps survive on every page, but the retrieval API takes only\(user\_query, user\_id\)\(retriever\.py:92\-\-131\), so even existing metadata is not addressable at query time\. Fact\-level supersession would require keeping LTM as a fact\-graph with bidirectional links to source pages—i\.e\., not summarizing\.

##### Thought experiment: adding slot keys to Mem0\.

Suppose we want Mem0 to supersede “User likes pizza” with “User likes sushi” while still being able to answer “what foods did the user previously prefer?”\.

1. 1\.m\.add\(‘‘User likes pizza’’, metadata=\{‘‘slot\_key’’: ‘‘food\_pref’’\}\)stores the entry with the custom field retained \(main\.py:401, 985\)\.
2. 2\.m\.add\(‘‘User likes sushi’’, …\)enters the LLM UPDATE\-decision step \(main\.py:496\-\-521;prompts\.py:175\-\-323\)\. The prompt reasons over*semantic similarity*, not slot\-key match; the LLM may chooseUPDATE\(overwriting pizza\),ADD\(siblings with no link\), orDELETE\. There is no downstream representation for “both kept, one inactive”\.
3. 3\.Forcing slot\-key supersession requires forking\_add\_to\_vector\_storeto \(a\) query existing entries by slot\-key filter, \(b\) bypass the LLM UPDATE step on slot match, and \(c\) emit the new entry taggedis\_active=Truewhile marking the old oneis\_active=Falsewithout deleting it—a fundamental departure from the replace\-payload semantics ofmain\.py:1142\-\-1194\.
4. 4\.At query time, returning only the active entry requires a filter\{‘‘is\_active’’: True\}; returning the historical entry requires the opposite filter\. The caller must therefore classify query intent before invokingm\.search, and Mem0 has no built\-in query\-intent classifier\.
5. 5\.A complete implementation now needs a query\-intent classifier, a slot\-key indexer, a deactivate\-and\-add update path, and a confidence\-aware reranker for soft supersession \(the LLM extraction step is probabilistic\)\. At this point the added components reproduce FR’s pipeline atop Mem0’s vector store rather than extending Mem0\.

Adding event\-time, slot keys, or retraction flags to any of these systems closes a notational gap, not a behavioral one\.

## Appendix FSlot\-Key Supersession: Extended Examples

Slot keys are normalized \(subject, attribute\) pairs for categories with*replace*semantics:

- •“User likes pizza”→\\to\(user, food\_preference\)
- •“User likes sushi”→\\tohigh\-confidence supersession
- •“User lives in Istanbul”→\\to\(user, current\_city\)
- •“User is thinking about moving to London”→\\tolow\-confidence\(both survive\)
- •“User moved to London”→\\tohigh\-confidence supersessionof Istanbul

For categories with*accumulate*semantics \(Identity, Relational\), supersession requires explicit contradiction with high confidence\.

## Appendix GMulti\-Reference\-Frame Temporal Sensitivity

Three temporal clocks:Absolute time\(calendar clock\): governs Logistical decay and deadline proximity\.Relative time\(session clock\): time since last session; governs Relational Bonds and Hobbies \(dormancy detection\)\.Conversational frequency: how often a fact appears across sessions; modulates base decay rate downward\.

Per\-category routing: Logistical→\\toprimarily absolute time; Relational→\\tosession gaps; Obligations→\\todeadline proximity; Identity→\\tonear\-zero sensitivity; Hobbies→\\torelative time; Preferences→\\toabsolute time\.

## Appendix HNumeric Preservation: Detailed Mechanisms

Loss Point 1: Deduplication Resolution\.When the dedup LLM marks a new edge as duplicate of an existing edge, the system keeps the old \(often generic\) edge\.Loss Point 2: Bulk Deduplication Canonical Selection\.Canonical selected by smallest UUID—arbitrary\.

Multi\-stage numeric rescue:\(1\) Pool\-stage exemption from expiry filter for monetary/quantity edges\. \(2\) Pool\-stage exemption from supersession filter\. \(3\) Reranking\-stage floor guarantee \(0\.95×0\.95\\timessemantic score for numeric edges with graphiti\_score≥0\.85\\geq 0\.85\)\. Combined: AV8 recovered from 81% to 94%\.

## Reproducibility Supplement

The following appendices document development trajectory, detailed parameter analysis, and per\-mechanism findings\. They are included for reproducibility and are not required for evaluating the main contributions\.

Artifact release\.All code, evaluation results, and run logs supporting this paper are publicly archived at[https://doi\.org/10\.5281/zenodo\.20067778](https://doi.org/10.5281/zenodo.20067778)\(DOI:10\.5281/zenodo\.20067778\)\.

## Appendix IRate Calibration: The Squatting Phenomenon

The initial rate configuration spanned800×800\\times\(λ=0\.0001\\lambda=0\.0001for Identity toλ=0\.080\\lambda=0\.080for Logistical\):

Table 34:Activation survival at original800×800\\timesrate spread\.Categoryλ\\lambda\(per hr\)3\-mo activation6\-mo activationIdentity0\.00010\.8070\.649Relational0\.0010\.0980\.010Preferences0\.0100\.0000\.000Logistical0\.0800\.0000\.000This producedcategory hierarchy squatting: Identity facts permanently occupied top ranking positions regardless of semantic relevance\. In top\-5 results across all questions, Identity comprised 307/480 slots \(64%\)\.

Table 35:Rate spread calibration\.ConfigSpreadB\-MRR \(α\\alpha=0\.1\)Top\-5 Identity %Squatting?Original800×\\times0\.55964%SevereCompressed16×\\times0\.57152%ModerateFinal5\.3×\\times0\.566∼\{\\sim\}30%MinimalThe cognitive ontology’s competitive mid\-alpha performance is explained by accidental rate calibration: its slowest rate \(Procedural atλ=0\.003\\lambda=0\.003\) is high enough that no category squats at multi\-month timescales\. Its rate floor prevents squatting; our explicit calibration achieves the same effect deliberately\.

##### Half\-life feasibility intervals\.

To validate that chosen decay rates are not over\-tuned, we perform a univariate sensitivity analysis: for each of the1111categories we sweepλc\\lambda\_\{c\}over multipliers\{0\.25×,0\.33×,0\.5×,0\.67×,0\.8×,1\.0×,1\.25×,1\.5×,2\.0×,3\.0×,4\.0×\}\\\{0\.25\\times,0\.33\\times,0\.5\\times,0\.67\\times,0\.8\\times,1\.0\\times,1\.25\\times,1\.5\\times,2\.0\\times,3\.0\\times,4\.0\\times\\\}while holding all other categories fixed at default, and measure mean Jaccard@10 vs\. the unperturbed top\-10 across all516516LifecycleBench questions\. A multiplier is*feasible*if mean Jaccard@10≥0\.95\\geq 0\.95\. Ten of eleven categories tolerate the full\[0\.25×,4×\]\[0\.25\\times,4\\times\]sweep \(16×16\\timeswidth\); onlyRelational\_Bondsfails at0\.25×0\.25\\timesand tolerates\[0\.33×,4\.0×\]\[0\.33\\times,4\.0\\times\]\(12\.1×12\.1\\timeswidth\)\. Every default value sits in the interior of its feasibility region \(Table[36](https://arxiv.org/html/2609.10413#A9.T36)\), confirming the system is robust to the specific parameter choice and that no category sits on a sensitivity cliff\.

Table 36:Per\-category half\-life feasibility intervals \(mean Jaccard@10≥0\.95\\geq 0\.95overn=516n=516questions; pool composition cached, scoring re\-run per cell\)\. All defaults sit interior to their feasibility regions\.CategoryDefaultλ\\lambdaMin mult\.Max mult\.WidthIDENTITY\_SELF\_CONCEPT0\.00150\.00150\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesRELATIONAL\_BONDS0\.00150\.00150\.33×0\.33\\times4\.00×4\.00\\times12\.1×12\.1\\timesINTELLECTUAL\_INTERESTS0\.00200\.00200\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesHEALTH\_WELLBEING0\.00250\.00250\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesPROJECTS\_ENDEAVORS0\.00250\.00250\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesHOBBIES\_RECREATION0\.00350\.00350\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesPREFERENCES\_HABITS0\.00500\.00500\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesFINANCIAL\_MATERIAL0\.00550\.00550\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesOBLIGATIONS0\.00600\.00600\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesLOGISTICAL\_CONTEXT0\.00800\.00800\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\timesOTHER0\.00500\.00500\.25×0\.25\\times4\.00×4\.00\\times16\.0×16\.0\\times

## Appendix JPhase\-by\-Phase Development and Results

### J\.1Phase 2: Initial Validation \(8 personas, 112 questions\)

Table 37:Phase 2 per\-AV results\.Attack VectornnFull PassFull StaleUni PassUni StaleΔ\\DeltaAV11436%7%36%14%0ppAV21995%5%79%21%\+16ppAV32259%0%64%0%−\-5ppAV4956%22%44%33%\+12ppAV5862%0%62%0%0ppAV6862%0%62%0%0ppAV780%12%12%25%−\-12ppAV81681%0%88%6%−\-7ppAV9888%0%75%0%\+13ppOverall11263%4%62%11%\+1pp

### J\.2Between\-Phase Improvements

Phase 2→\\to3:Scale 8→\\to20 personas; per\-source score normalization; cross\-category supersession; world\-knowledge filter \(86%→\\to1\.4%\)\.

Phase 3→\\to4:Scale 20→\\to40 personas; retraction extraction; AV8 numeric rescue; date\-aware expiry filter; parallel evaluation \(12×\\timesspeedup\)\.

Phase 4→\\to5b:Multi\-stage numeric rescue; backward\-looking expiry bypass; date resolver future\-preference guard\.

Phase 5b→\\to5c:Identity/health supplementary extraction: 2,996 candidates→\\to388 retained \(13%\)\.

### J\.3Phase 3 Results \(20 personas, 257 questions\)

Table 38:Phase 3 overall results\.ConfigPassStaleMRRbaseline55%18%0\.480uniform61%15%0\.466no\_routing63%8%0\.449full66%6%0\.475

## Appendix KDetailed Findings from LifecycleBench Evaluation

Backward\-looking query detection\.Keyword patterns \(“before switching”, “used to”\) bypass the supersession filter, recovering 3 otherwise unreachable questions\.

Retraction filtering\.AV7 staleness drops from 25% to 12% with the retraction filter scanning for markers \(“plan is dead”, “scrapped”\)\.

Date\-aware expiry filtering\.Parses ISO dates, month\+day patterns, contextual months, and relative markers\. Category\-guarded \(Logistical, Obligations, Health only\) with 14\-day buffer\.

Category\-specificα\\alpha\.With uniformα=0\.3\\alpha=0\.3, AV8 drops to 12\.5%\. Category\-specific: Financial at 0\.05, Logistical at 0\.40\.

Semantic floors\.Near\-perfect semantic matches for stable categories are not buried by zero activation\. Financial floor 0\.97; Logistical floor 0\.00\. Hit@1: 19%→\\to31%\.

Pass\-by\-absence\.Both systems exhibit this on AV2\. FR: 50 cases \(expiry filter\); Mem0: 29 \(extraction failure\)\.

AV3 tradeoff decomposition\.77% extraction misses, 12% decay\-killed, 12% partial\.

## Appendix LScalability Analysis

Table 39:Projected scaling over 2 years\.MetricFlat RetentionLifecycle Mgmt\.Active edges \(retrievable\)∼\{\\sim\}30,000∼\{\\sim\}5,000–8,000Contradictions in top\-20∼\{\\sim\}3–5∼\{\\sim\}0Expired events in top\-20∼\{\\sim\}2–4∼\{\\sim\}0Context pollution rateGrows with timeStableFR’s stale token rate is 3\.0% versus Mem0’s 9\.0%\. At GPT\-4o pricing, FR saves $25\.12 per million queries in stale token costs alone\.

## Appendix MComposability

Fortunate Recall is a composable policy layer\. Existing Graphiti deployments can add behavioral classification without migrating data\. Components can be adopted incrementally\. The ontology can be extended for domain\-specific applications\. FluxMem’s structure selection and FR’s lifecycle policy are orthogonal and could compose\.

The AV3 improvement through supplementary extraction \(−\-16pp→\\to−\-9pp gap\) is empirical evidence: the lifecycle layer was unchanged, only extraction improved, and lifecycle\-managed retrieval immediately benefited\.

## Appendix NEnd\-to\-End Evaluation Details

### N\.1Methodology

For each of 516 questions, each system’s top\-10 facts are fed to GPT\-5\.4 \(gpt\-5\.4\[[22](https://arxiv.org/html/2609.10413#bib.bib22)\]; temperature=0, max\_tokens=500\) with a system prompt restricting answers to provided facts\. Claude Sonnet \(claude\-sonnet\-4\-6\) judges correctness \(CORRECT, PARTIAL, WRONG, ABSTAIN\) and confabulation\. No Anthropic models for generation\. Memory pipelines \(FR\-Bank ingestion/distillation, Mem0 default extraction, Memory\-R1 extraction, A\-MEM evolution, Mem0\-mini ablation\) usegpt\-4\.1\-mini\(versioned:gpt\-4\.1\-mini\-2025\-04\-14\); Mem0’s default extraction usesgpt\-4\.1\-nano; Kimi K2\.5 cross\-generator validation useskimi\-k2\.5via the Moonshot API\. The LongMemEval\-S judge under the Wu et al\. protocol isgpt\-4o\-2024\-08\-06, as reported in §[6](https://arxiv.org/html/2609.10413#S6)\.

### N\.2Staleness\-Confabulation Causal Chain

Table[40](https://arxiv.org/html/2609.10413#A14.T40)partitions the 1,032 end\-to\-end queries by retrieval\-context cleanliness: clean contexts yield 18–30% confabulation, while stale contexts \(any outdated fact in the top\-10\) jump to 72–78%, establishing the causal link between lifecycle filtering and downstream answer quality\.

Table 40:Staleness predicts confabulation end\-to\-end\.Retrieval contextnnConfab\.CorrectClean \(staleness = 0\)85118–30%20–25%Stale \(staleness\>\>0\)18172–78%5–10%
### N\.3Reasoning Token Overhead

Table[41](https://arxiv.org/html/2609.10413#A14.T41)shows that stale retrieval contexts induce only a modest≈10\\approx 10% reasoning\-token increase on GPT\-5\.4, so the confabulation gap between FR and Mem0 is a lifecycle architecture effect, not a test\-time compute effect\.

Table 41:Reasoning token overhead by context staleness\.SystemContextAvg output tokensAvg reasoning tokensFRClean \(nn=474\)118\.783\.5FRStale \(nn=42\)133\.592\.7Mem0Clean \(nn=377\)118\.180\.5Mem0Stale \(nn=139\)129\.189\.7
### N\.4Abstain Analysis

FR\-Graphiti abstains on 227/516 queries \(44\.0%\) and FR\-Bank on 217/516 \(42\.1%\); Mem0 abstains on 148/516 \(28\.7%\)\. FR\-Bank therefore abstains 69 more times than Mem0 and FR\-Graphiti 79 more times\. The pre\-registered untyped ablation \(Appendix[AD](https://arxiv.org/html/2609.10413#A30)\) establishes what those extra abstentions are made of: they are drawn almost entirely from would\-be wrong or fabricated answers rather than from correct ones\.

### N\.5Full Per\-Attack\-Vector Breakdown \(GPT\-5\.4\)

Table 42:Full per\-AV E2E response quality on GPT\-5\.4, all five systems\.FR\-BankFR\-GraphitiMemoryOSMemory\-R1Mem0AVnnCorrConfCorrConfCorrConfCorrConfCorrConfAV17544\.07\.132\.022\.018\.743\.240\.016\.324\.056\.5AV27516\.034\.86\.742\.94\.067\.56\.761\.26\.767\.3AV39434\.011\.116\.011\.114\.918\.822\.313\.323\.411\.3AV44447\.710\.738\.618\.520\.518\.827\.317\.429\.538\.2AV5400\.040\.00\.030\.00\.052\.62\.522\.62\.546\.2AV6452\.275\.00\.072\.22\.252\.42\.259\.10\.058\.3AV74037\.533\.327\.533\.37\.581\.22\.590\.02\.591\.4AV86366\.77\.865\.17\.430\.217\.438\.19\.149\.213\.6AV94012\.535\.712\.513\.312\.515\.415\.038\.112\.535\.0All51631\.222\.422\.923\.913\.240\.819\.631\.518\.645\.1

Table 43:Full per\-AV E2E response quality on GPT\-5\.4: A\-MEM and Mem0 \(gpt\-4\.1\-mini\), regenerated from the raw per\-question judge records\.*Correction:*the per\-AV Correct cells of this table in the submitted version were stale—weighting them bynAVn\_\{\\mathrm\{AV\}\}gave17\.817\.8\(A\-MEM\) and23\.923\.9\(Mem0\-mini\) rather than the stated aggregates\. The “All” aggregates were already correct; the regenerated per\-AV cells below weight\-average to them exactly \(Appendix[AI](https://arxiv.org/html/2609.10413#A35)\)\.A\-MEMMem0 \(gpt\-4\.1\-mini\)AVnnCorrConfCorrConfAV17528\.055\.242\.735\.8AV2755\.371\.96\.769\.4AV39422\.310\.025\.510\.8AV44431\.840\.043\.230\.3AV5400\.053\.80\.036\.7AV6450\.068\.46\.757\.5AV7405\.078\.920\.045\.2AV86344\.417\.561\.94\.3AV94017\.525\.027\.523\.1All51618\.847\.027\.333\.8
### N\.6Per\-AV End\-to\-End Confabulation \(Three Systems\)

Table 44:Per\-AV end\-to\-end confabulation \(three systems\), regenerated from the raw per\-question judge records \(gpt54\_nr,n=516n=516\)\. Corr\. = CORRECT /nAVn\_\{\\mathrm\{AV\}\}; confab\. = confabulations / non\-abstaining responses\. AV7: both Mem0 and MR1 cause\>90%\{\>\}90\\%confabulation without structural retraction filtering\.*Correction:*the FR and Mem0 columns of this table in the submitted version were stale \(they matched no current run; the Memory\-R1 column was already correct\) and are replaced here in full \(Appendix[AI](https://arxiv.org/html/2609.10413#A35)\)\.Attack VectornnFR\-Bank corr\.FR\-Bank confab\.MR1 corr\.MR1 confab\.Mem0 corr\.Mem0 confab\.AV1 Superseded Pref\.7544\.0%7\.1%40\.0%16\.3%24\.0%56\.5%AV2 Expired Logistics7516\.0%34\.8%6\.7%63\.3%6\.7%67\.3%AV3 Stable Identity9434\.0%11\.3%22\.3%14\.7%23\.4%11\.3%AV4 Multi\-Version4447\.7%10\.7%27\.3%17\.4%29\.5%38\.2%AV5 Broad Query400\.0%46\.7%2\.5%22\.6%2\.5%46\.2%AV6 Cross\-Session452\.2%75\.0%2\.2%59\.1%0\.0%61\.1%AV7 Selective Forgetting4037\.5%33\.3%2\.5%95\.0%2\.5%91\.4%AV8 Numeric Preserv\.6366\.7%7\.8%38\.1%12\.1%49\.2%13\.6%AV9 Soft Supersession4012\.5%35\.7%15\.0%38\.1%12\.5%35\.0%

### N\.7Case Studies

14 cases where FR produced CORRECT responses and Mem0 produced WRONG responses with confabulation\. Examples: Mem0 surfaces “Jake is vaping” \(retracted—user quit\); “Chenoa’s old truck” \(superseded by new vehicle\); “Jerome planning owner\-operator business” \(abandoned\)\. In each case, FR’s lifecycle filtering removed the outdated fact before the downstream model could anchor on it\.

### N\.8Extended Cross\-System Analysis

Architectural gaps cannot be closed by model upgrades\.Model quality affects extraction recall—how many facts are stored—but cannot address architectural absences\. No extraction model can add event\-time expiry to a flat vector store \(AV2: FR\-Graphiti 93%, FR\-Bank 88\.0% vs Mem0 65%\), impose category\-specific decay \(AV1, AV4\), or suppress explicitly retracted plans \(AV7: FR\-Graphiti 40% vs Mem0 5%, 80% staleness; FR\-Bank’s 5% retrieval pass on AV7 is the intended suppression behavior described in §[6](https://arxiv.org/html/2609.10413#S6)\)\. These are structural capabilities requiring architectural support, not better prompting\.

Memory\-R1 validates that learned operations cannot substitute for missing mechanisms\.Memory\-R1’s RL\-trainable action space \{ADD, UPDATE, DELETE, NOOP\} achieves strong retrieval quality \(MRR 0\.816, above FR\-Graphiti’s 0\.478 though below FR\-Bank’s 0\.830\) and performs well on stable identity retrieval \(AV3: 94%, above FR\-Graphiti’s 78% but below FR\-Bank’s 97%\)\. However, the action space contains no event\-time expiry operation \(AV2: FR\-Graphiti 93%, FR\-Bank 88\.0% vs MR1 75%, 25% staleness\), no structured retraction mechanism \(AV7: FR\-Graphiti 40% vs MR1 15%, 42% staleness\), and no numeric preservation pipeline \(AV8: FR\-Graphiti 94%, FR\-Bank 84\.1% vs MR1 57%\)\. These are vocabulary gaps in the action space—no reward signal can induce an action that does not exist\. The approaches are complementary: FR’s ontology provides the structural prior over which lifecycle policy applies; RL optimizes when to apply it\.

AV3 gap halved through supplementary extraction—confirming composability\.The gap narrowed from−\-16pp to−\-9pp through targeted identity/health re\-extraction \(388 supplementary edges\)\. Failure decomposition showed 77% of AV3 failures were extraction misses—the lifecycle layer was unchanged, only extraction quality improved, and AV3 immediately benefited\. This empirically validates FR’s composability thesis\.

Routing emerges at scale\.Category\-aware retrieval routing shows zero differential at 8 personas; \+3pp at 20; \+6pp at 40\. The mechanism requires sufficient category density to outperform global semantic search\.

AV7 improvement trajectory\.AV7 \(selective forgetting\) improved from 0% \(Phase 2\) to 10% \(Phase 3\) to 28% \(Phase 5b\) to 40% \(Phase 5c\)\. Retraction\-aware extraction and supplementary identity/health extraction drove the most dramatic improvement across five phases\. End\-to\-end, FR\-Bank outperforms Mem0 by\+35\+35pp on selective forgetting \(37\.5% vs\. 2\.5% correct\)\.

Staleness predicts confabulation end\-to\-end\.Cross\-referencing retrieval staleness with E2E outcomes: when retrieval produces stale context, 72–78% of responses are contaminated \(consistent across both systems\)\. When retrieval is clean, confabulation drops to 18–30%\. The degradation function is consistent; what FR controls is the input distribution\.

AV7 confabulation without lifecycle management\.Mem0’s context causes GPT\-5\.4 to confidently discuss explicitly retracted plans on 91\.4% of AV7 queries\. FR\-Bank reduces this to 33\.3% \(Table[44](https://arxiv.org/html/2609.10413#A14.T44)\); the32\.5%32\.5\\%reported at this point in the submitted version is MemoryOS’s AV7 abstain rate, not FR’s confabulation rate\. On selective forgetting, a memory system without retraction filtering produces a downstream LLM that almost always actively misleads the user about their own stated intentions\.

Five\-system degradation function\.Memory\-R1’s stale context produces 89\.8% confabulation versus 18\.2% with clean context—a \+71\.6pp gap consistent with FR’s and Mem0’s degradation rates\. On AV7, Memory\-R1’s context causes 90\.0% confabulation, identical to Mem0’s 91\.4%, confirming that without structural retraction filtering, learned DELETE operations provide negligible downstream protection\.

Safe response hierarchy\.The safe response rank order \(FR\-Bank\>\>FR\-Graphiti\>\>Memory\-R1\>\>Mem0\) is generator\-invariant\. Kimi K2\.5 is systematically 6\.9–12\.3pp less safe than GPT\-5\.4 across every system \(FR\-Bank 73\.3%→\\to61\.0%, FR\-Graphiti 66\.9%→\\to59\.2%, Memory\-R1 58\.1%→\\to51\.3%, Mem0 47\.3%→\\to40\.2%\)\. This uniform∼\{\\sim\}10pp shift reflects Kimi’s stronger preference for answering over abstaining without a commensurate gain in correct answers\.

Assistant\-generated content is tractable but still the weakest category\.On LongMemEval\-S the single\-session\-assistant category reaches 75\.4% pass@10 \(mean over 10 reruns; 78\.6% max\), up from an initial 50\.0% before the raw\-text fallback, answer\-time inflation, and routing changes described in Appendix[AA](https://arxiv.org/html/2609.10413#A27)\. FR\-Bank’s extraction pipeline still targets user facts primarily; assistant\-generated structured content depends on the fallback path\.

Note on FR\-Graphiti comparison\.The FR\-Graphiti rows \(32\.1% pass@10\) in Table[17](https://arxiv.org/html/2609.10413#A4.T17)represent the decay engine comparison from the original evaluation, which used Graphiti’s pre\-built edges with different decay policies\. FR\-Bank re\-extracts from raw conversations with a fundamentally different pipeline\.

Cross\-benchmark validation\.FR\-Bank achieves strong results on LongMemEval\-S \(75\.2% on the full 500\-question canonical setup, the first peer\-reviewable result under the exact Wu et al\. rubric\), LifecycleBench \(76\.9%\), and the 234\-question LongMemEval oracle POC subset \(79\.5%\)\. No existing system demonstrates competitive performance on both a standard retrieval benchmark and a lifecycle\-aware temporal disambiguation benchmark simultaneously\. This cross\-benchmark validation confirms that lifecycle management is complementary to retrieval quality, not a tradeoff\.

Staleness impact is modulated by retrieval recall\.At low recall \(FR\-Graphiti, 75% Hit@5\), staleness prevention is critical—the correct fact is often absent, leaving the LLM to anchor on stale alternatives\. At high recall \(FR\-Bank, 97% Hit@5\), the correct fact is almost always present, and the LLM can resolve contradictions even with moderate staleness\. The optimal system minimizes staleness and maximizes recall; FR\-Bank achieves the latter\.

## Appendix OMem0 Comparison Methodology

Mem0 v1\.0\.5 \(Apache 2\.0\), 100% default configuration: gpt\-4\.1\-nano extraction, text\-embedding\-3\-small embeddings, Qdrant vector store\. The only non\-default setting was enabling disk persistence, as Mem0’s default in\-memory storage does not survive between process invocations\. All 40 personas \(1,400 sessions\) were ingested throughm\.add\(\)API with raw conversation turns, and all 516 questions evaluated with the same Claude Sonnet LLM judge\. Default extraction model produced frequent JSON parse errors during UPDATE and DELETE operations, causing some lifecycle updates to fail silently\.

The Mem0 extraction prompt is the library default \(v1\.0\.5\); no custom system prompt was used\. All 1,400 sessions were ingested viam\.add\(\)with raw conversation turns as input\.

Stronger\-extractor ablation \(gpt\-4\.1\-mini\) result\.To isolate extraction quality from architectural capability, we re\-evaluate Mem0 with gpt\-4\.1\-mini replacing the default gpt\-4\.1\-nano extractor \(configuration in Appendix[P\.2](https://arxiv.org/html/2609.10413#A16.SS2)\)\. The stronger model raises AV\-pass from 61\.0% to 67\.1% \(\+6\.1\+6\.1pp\) and reduces confabulation from 45\.1% to 33\.8% \(−\-11pp\), confirming extraction quality as a genuine bottleneck\. However, structural gaps persist: AV2 \(expired logistics\) remains at 61% versus FR\-Bank’s 88\.0%, and AV7 \(selective forgetting\) at 20% versus FR\-Graphiti’s 40%, because no extraction model can add event\-time expiry or retraction filtering to a flat vector store\. Mem0 with gpt\-4\.1\-mini now matches Memory\-R1 \(67\.1% vs 66\.9%\)—two architecturally distinct systems hitting the same ceiling in the absence of lifecycle mechanisms\.

## Appendix PMemory\-R1 Comparison Methodology

Memory\-R1\[[10](https://arxiv.org/html/2609.10413#bib.bib10)\]proposes a two\-agent RL pipeline: a Memory Manager that decides \{ADD, UPDATE, DELETE, NONE\} operations on a flat JSON memory bank, and an Answer Agent that retrieves candidates via embedding similarity and applies Memory Distillation\. The original paper trains both agents with GRPO on 152 QA pairs from LoCoMo using LLaMA\-3\.1\-8B\-Instruct\.

Our reimplementation uses GPT\-4\.1\-mini for both the Memory Manager and Answer Agent—substantially stronger than the paper’s base model, providing an upper bound on pre\-RL performance\. Fact extraction uses GPT\-4o\-mini \(exact match with the paper\)\. Embeddings use text\-embedding\-3\-small \(1536\-dim\)\. The Memory Manager receives new facts and the 15 most similar existing memories, returning a complete updated memory list in JSON format\. The Answer Agent retrieves 60 candidates via cosine similarity and distills to 10 via LLM filtering\.

Ingestion statistics\.Across 40 personas \(1,400 sessions\), the Memory Manager processed 65,411 total operations: 5,083 ADD \(7\.8%\), 1,121 UPDATE \(1\.7%\), 809 DELETE \(1\.2%\), and 58,398 NONE \(89\.3%\)\. The high NONE rate indicates the manager correctly identifies most extracted facts as already present\. Final memory bank: 4,278 entries \(avg 107/persona\)\.

Rationale for GPT\-4\.1\-mini backbone\.Using a stronger backbone provides an upper bound: if Memory\-R1’s architecture with a strong backbone still exhibits structural gaps \(AV2, AV7, AV8\), these gaps are attributable to the action space vocabulary, not model capability\.

Prompts\.The Memory Manager system prompt follows the published Memory\-R1 specification: it receives the current memory bank and a list of new facts extracted from the conversation, and returns the updated bank as a JSON list after applying \{ADD, UPDATE, DELETE, NONE\} operations\. The Answer Agent prompt instructs the model to answer based solely on retrieved memories\. Both prompts are included verbatim in the released evaluation code\.

MemoryOS evaluation\.MemoryOS\[[9](https://arxiv.org/html/2609.10413#bib.bib9)\]implements an OS\-inspired hierarchical memory architecture with cognitive categories \(episodic, semantic, procedural\) and progressive summarization through short\-term, mid\-term, and long\-term memory tiers\. We evaluate the published implementation with GPT\-4\.1\-mini as the backbone\. MemoryOS performs approximately 1,500 LLM calls per 35\-session persona during ingestion compared to FR\-Bank’s∼\{\\sim\}50—a30×30\\timesingestion compute cost differential\.Philosophical positioning\.Memory\-R1 asks: “Can we learn the optimal memory policy end\-to\-end?” Fortunate Recall asks: “Can we design an interpretable memory policy that works from day one?” These are complementary—our ontology could serve as initialization, reward shaping, or structural constraint for an RL\-based manager\.

### P\.1A\-MEM Comparison Methodology

A\-MEM\[[4](https://arxiv.org/html/2609.10413#bib.bib4)\]implements a Zettelkasten\-style linked\-note memory system with LLM\-driven note evolution\. We evaluate the published implementation with gpt\-4\.1\-mini as the backbone LLM and text\-embedding\-3\-small for embeddings, matching the extraction model used for Memory\-R1 and Mem0 \(gpt\-4\.1\-mini\)\. The default evolution threshold \(evo\_threshold=100\) was retained for paper\-faithful evaluation\. ChromaDB was used as the persistent vector store with one collection per persona\. Sequential per\-persona ingestion was required because A\-MEM’schromadb\.Client\(\)\.reset\(\)is process\-global, destroying all collections when called\.

Detailed result and benchmark\-independence interpretation\.A\-MEM\[[4](https://arxiv.org/html/2609.10413#bib.bib4)\]represents the Zettelkasten paradigm: linked\-note memory with LLM\-driven evolution but no temporal dynamics, forgetting, or supersession\. Evaluated with gpt\-4\.1\-mini and the paper’s default evolution threshold, A\-MEM achieves 65\.3% pass with the highest retrieval recall of any evaluated system \(87\.6% Hit@5\) but also the highest staleness \(30\.4%\) and worst end\-to\-end confabulation \(47\.0%\)\. High recall without lifecycle management actively hurts downstream performance: the more stale facts surfaced, the more the downstream model confabulates\. A\-MEM was designed independently and published at NeurIPS 2025; it was not among the systems used to derive LifecycleBench’s attack vectors, yet its evaluation produces failure patterns fully consistent with the benchmark’s predictions, confirming that the attack vectors test architectural properties of the problem domain rather than FR\-specific capabilities\.

### P\.2Mem0 \(gpt\-4\.1\-mini\) Ablation Methodology

To isolate extraction quality from architectural capability, we re\-evaluated Mem0 with gpt\-4\.1\-mini replacing the default gpt\-4\.1\-nano extraction model\. All other settings matched the default Mem0 evaluation \(Appendix[O](https://arxiv.org/html/2609.10413#A15)\): text\-embedding\-3\-small embeddings, Qdrant vector store with disk persistence, identical ingestion viam\.add\(\)API\. Sequential per\-persona ingestion was required due to Qdrant local\-mode SQLite lock contention under parallelism\.

## Appendix QFortunate Recall–Specific Metrics

Pass rate\(primary\)\.Staleness penalty\(primary\)\.Positional staleness exposure\(proposed\): fraction of queries with stale facts in high\-attention positions\. FR: 14\.0%, Mem0: 37\.2%\.Weighted staleness risk\(proposed\): attention weights of 3\.0/1\.0/2\.0 for ranks 1–3/4–7/8–10\. FR: 0\.51, Mem0: 1\.84\. Future work: temporal calibration, anticipatory precision/recall, user model accuracy over time\.

## Appendix RLiterature Positioning

Table 45:Literature positioning with empirical results\.SystemContributionGaps This Work FillsZep/GraphitiTemporal KG, hybrid retrievalNo behavioral ontology; no lifecycle policies; no anticipatory activationA\-MEMZettelkasten memoryNo temporal dynamics; no forgetting; LLM\-heavy runtimeMemoryBankEbbinghaus curvesSingle uniform curve; no graph; single temporal frameMem0Clean API, vector storeNo lifecycle; no categories\.*61% pass, 27% stale*MemGPT/LettaTiered contextLLM\-driven policy; no lifecycle in archivalMemoryOSOS\-inspired hierarchyCognitive not behavioral; no per\-category lifecycleMemory\-R1RL\-learned operationsOpaque; no behavioral structure; no multi\-clockFR\-BankBehavioral lifecycle76\.9% pass; 22\.4% confab; leads 4/9 AVs\+\+AV9 tie

## Appendix SFull Alpha Sweep

The following table reports the fullα\\alphasweep across behavioral, uniform, and cognitive decay configurations on LongMemEval\.

Table 46:Full alpha sweep on LongMemEval\.α\\alphaB\-MRRU\-MRRC\-MRRWinner0\.00\.56180\.56180\.5618Tie0\.10\.56590\.56290\.5642Behavioral0\.20\.55000\.58280\.5608Uniform0\.30\.53470\.55160\.5367Uniform0\.40\.50320\.51450\.5221Cognitive0\.50\.50200\.48810\.5032Cognitive0\.60\.47690\.45280\.4777Cognitive0\.70\.44700\.41310\.4525Cognitive0\.80\.37110\.36190\.3897Cognitive0\.90\.29030\.31590\.3242Cognitive1\.00\.04610\.16860\.0484Uniform
## Appendix TFine\-Grained Alpha Sweep with Statistical Tests

The following table reports the fine\-grainedα\\alphasweep with pairedtt\-test significance and effect sizes\.

Table 47:Fine\-grained alpha sweep\. All p\-values fail Bonferroni correction \(p<0\.0056p<0\.0056\)\. All\|d\|<0\.2\|d\|<0\.2\.α\\alphaB\-MRRU\-MRRC\-MRRΔ\\Delta\(B−\-U\)pp95% CIdd0\.000\.5618\.5618\.5618\+\.00001\.000\[\+\.000, \+\.000\]\.0000\.025\.5600\.5705\.5636−\-\.0105\.016\[−\-\.024,−\-\.002\]−\-\.1790\.050\.5767\.5795\.5785−\-\.0027\.221\[−\-\.018, \+\.013\]−\-\.0360\.075\.5756\.5761\.5839−\-\.0005\.653\[−\-\.016, \+\.015\]−\-\.0070\.100\.5659\.5629\.5642\+\.0030\.706\[−\-\.015, \+\.022\]\+\.0320\.125\.5592\.5596\.5676−\-\.0004\.433\[−\-\.018, \+\.017\]−\-\.0050\.150\.5593\.5632\.5667−\-\.0039\.745\[−\-\.031, \+\.021\]−\-\.0310\.175\.5621\.5705\.5641−\-\.0085\.338\[−\-\.039, \+\.021\]−\-\.0560\.200\.5519\.5828\.5608−\-\.0309\.026\[−\-\.065, \+\.002\]−\-\.182

## Appendix UCategory\-Specific Parameters

Table[48](https://arxiv.org/html/2609.10413#A21.T48)reports the per\-category blending weightsαc\\alpha\_\{c\}and semantic floors used throughout all experiments; per\-category decay ratesλc\\lambda\_\{c\}are reported in Appendix[V](https://arxiv.org/html/2609.10413#A22)\.

Table 48:Category\-specific blending weightsα\\alphaand semantic floors\. Emotional loading is a transient activation modifier applied to other categories rather than a standalone memory category; the listedα\\alphagoverns the decay of the loading signal itself, not a separate row of the ontology\.Categoryα\\alphaFloorRationaleFinancial & Material0\.050\.97Monetary facts rarely become less trueIdentity & Self\-Concept0\.100\.95Identity changes slowlyHealth & Wellbeing0\.100\.95Medical facts persistRelational Bonds0\.100\.95Family changes slowlyIntellectual Interests0\.150\.90Interests fairly stablePreferences & Habits0\.200\.85Preferences shift graduallyHobbies & Recreation0\.200\.92Raised for numeric rescueProjects & Endeavors0\.300\.75Projects change oftenObligations0\.350\.70Time\-boundEmotional Loading \(signal\)0\.400\.00Transient modifier; fully decaysLogistical Context0\.400\.00Expired facts must be suppressible
## Appendix VDecay Rates

Table 49:Per\-category decay rates\. Spread:5\.3×5\.3\\times\.Categoryλ\\lambda\(per hr\)Half\-life1\-mo6\-moIdentity & Self\-Concept0\.001519d34%0\.2%Relational Bonds0\.001519d34%0\.2%Intellectual Interests0\.002014d24%0\.02%Health & Wellbeing0\.002512d17%<\{<\}0\.01%Projects & Endeavors0\.002512d17%<\{<\}0\.01%Hobbies & Recreation0\.00358d8%<\{<\}0\.01%Preferences & Habits0\.00506d3%≈\{\\approx\}0%Financial & Material0\.00555d2%≈\{\\approx\}0%Obligations0\.00605d1%≈\{\\approx\}0%Logistical Context0\.00804d0\.3%≈\{\\approx\}0%Other0\.00506d12%≈\{\\approx\}0%For soft\-clustered facts:λeff=\(∑cwc/λc\)−1\\lambda\_\{\\text\{eff\}\}=\\left\(\\sum\_\{c\}w\_\{c\}/\\lambda\_\{c\}\\right\)^\{\-1\}\.

TheOtherrow is reported here at the deployed valueλ=0\.0050\\lambda=0\.0050, matching Table[36](https://arxiv.org/html/2609.10413#A9.T36)and the released runs; the submitted version printed0\.00300\.0030in this table only\. The discrepancy is immaterial to every reported result:Otheris the primary category for 16 of 12,968 active entries \(0\.12%0\.12\\%\), no LifecycleBench question hasOtheras its gold category, and the only two questions that retrieve anOtherentry are outcome\-invariant under either value\.

## Appendix WCross\-System Outcome Matrix and Positional Staleness

The two tables below report the paired outcome matrix between FR\-Bank and Mem0 across all 516 questions, and per\-AV positional staleness exposure \(high\-attention zone\)\.

Table 50:Cross\-system outcome matrix \(516 questions\)\.Mem0 passMem0 absenceMem0 failFR pass218494FR absence112415FR fail56193Table 51:Per\-AV positional staleness exposure \(high\-attention zone\)\.AVnnFR exp\.Mem0 exp\.Δ\\DeltaAV74010\.0%90\.0%\+80ppAV17530\.7%72\.0%\+41ppAV44429\.5%63\.6%\+34ppAV64522\.2%53\.3%\+31ppAV2758\.0%44\.0%\+36ppAV3941\.1%1\.1%0ppOverall51614\.0%37\.2%\+23pp
## Appendix XAblation Summary

The following table summarizes the component\-level ablation results from Phase 2 \(8 personas\)\.

Table 52:Ablation results \(Phase 2, 8 personas\)\.ComponentLifecycleBench EffectLongMemEvalFull system63% pass, 4% stale0\.566 MRR−\-Top\-10 window \(→\\totop\-5\)−\-9pp passN/A−\-Cat\-specificα\\alpha\(→\\to0\.3\)−\-24\.6pp passN/A−\-Semantic floorHit@1: 31%→\\to19%N/A−\-Retraction filterAV7 stale: 12%→\\to25%N/A−\-Backward\-looking detection−\-3 questionsN/AUniform only \(no ontology\)62% pass, 11% staleNo change

## Appendix YPositional Utilization at Retrieval Depth

Replication of Liu et al\.\[[15](https://arxiv.org/html/2609.10413#bib.bib15)\]on Claude Sonnet \(2026\) at 50\-document scale \(n=3,500n=3\{,\}500\): point\-biserialr=−0\.009r=\-0\.009,p=0\.65p=0\.65, 95% CI\[−0\.044,\+0\.022\]\[\-0\.044,\+0\.022\]\. No significant positional effect at retrieval depths relevant to our evaluation\. The dramatic U\-curves from 2023 models are not reproducible on 2026 frontier models\.

## Appendix ZFR\-Bank Architecture and Methodology

FR\-Bank replaces Graphiti with a standalone embedding\-indexed memory bank \(∼\{\\sim\}780 lines\)\.Ingestion:One GPT\-4\.1\-mini call per turn for combined extraction and classification\. Near\-duplicates \(cosine\>0\.95\>0\.95\) skipped; numeric facts exempt\.Supersession:Instance\-qualified slot\-keys\. Replace\-semantics categories: threshold 0\.8\. Accumulate\-semantics: threshold 0\.95\.Retrieval:\(1\) Cosine top\-60, \(2\) BM25 top\-20, \(3\) category\-forced top\-20, \(4\) merge/dedup, \(5\) staleness\-aware distillation top\-20, \(6\) lifecycle filters, \(7\) blended scoring, \(8\) top\-10 output\.

Ingestion statistics\.18,936 total entries; 12,968 active \(31\.5% deactivated\)\. Average 324\.2 active per persona\. \(The submitted version reported 5,344 / 3,892 / 133\.6, a stale proof\-of\-concept snapshot; the values here are verified against the releasedlifecycle\_banks/\.\)

## Appendix AALongMemEval FR\-Bank Evaluation Methodology

Per\-question banks are created for the oracle format\. Both user and assistant turns are ingested\. A raw\-text BM25 fallback handles zero\-extraction questions\. The full retrieval pipeline runs with identical parameters to LifecycleBench\. Answer generation usesgpt\-4o\-mini\(temperature 0, max\_tokens 300\) over the top\-10 retrieved facts; fact extraction usesgpt\-4\.1\-mini\.

##### Per\-question banks are the standard oracle protocol\.

The per\-question bank structure is not an FR\-Bank design choice: it is the evaluation protocol defined by LongMemEval\[[1](https://arxiv.org/html/2609.10413#bib.bib1)\]and matched by LoCoMo\[[13](https://arxiv.org/html/2609.10413#bib.bib13)\], both of which score each question against its own conversation haystack rather than against a single persistent memory store\. Every peer\-reviewed LongMemEval result \(Wu et al\. ICLR 2025; RMM ACL 2025\[[3](https://arxiv.org/html/2609.10413#bib.bib3)\]\) is produced under the same per\-question setup, so FR\-Bank’s 75\.2% on LongMemEval\-S and 79\.5% on the 234\-question oracle POC subset are directly comparable to those references\. The fully persistent evaluation setting—one memory store accumulating 35 multi\-session conversations per persona and 516 lifecycle\-sensitive queries against that same store—is exactly the regime measured by LifecycleBench, where FR\-Bank reaches 76\.9% pass with 15\.5% staleness\.

##### Judge protocol \(Wu et al\. verbatim\)\.

All reported LongMemEval\-S numbers usegpt\-4o\-2024\-08\-06as the judge at temperature 0, with the question\-type routing and prompt templates taken verbatim from Figure 10 of Wu et al\. \(ICLR 2025\)\. Five templates are used, one per task type:

- •Default\(single\-session\-user,single\-session\-assistant,multi\-session\): marks “yes” when the model response contains the correct answer or all intermediate steps; “no” when only a subset of the required information is present\.
- •temporal\-reasoning: default template plus explicit off\-by\-one tolerance—responses predicting, e\.g\., 19 days when the answer is 18 are marked correct\.
- •knowledge\-update: responses that contain prior information alongside the updated answer are marked correct provided the updated answer is present\.
- •single\-session\-preference: rubric\-based partial credit—the response need not cover every rubric point but must correctly recall and utilise the user’s personal information\.
- •abstention\(routed when the question id contains\_abs\): marks “yes” only if the model correctly identifies the question as unanswerable\.

Each judge call is deterministic \(max\_tokens=10, temperature 0\) and the verdict is parsed from the presence of “yes” in the response\. Across 10 identical reruns, total pass rate moves within 74\.4–76\.6% \(stdev 0\.70pp; Table[15](https://arxiv.org/html/2609.10413#A4.T15)\), which we attribute to residual non\-determinism in the hosted judge endpoint rather than to our pipeline\.

##### Comparability note\.

Theevaluate\_qa\.pyroutine in the official LongMemEval release uses these same five templates\. The closest peer\-reviewed LongMemEval result prior to this work, RMM \(Tan et al\., ACL 2025\), substitutes Gemini\-1\.5\-Pro forgpt\-4o\-2024\-08\-06and replaces the five templates with a single generic prompt \(their Appendix D\.3\)\. Because neither the judge model nor the rubric matches, RMM’s 70\.4% and our 75\.2% are not measured on the same axis; we report them side\-by\-side only to flag that FR\-Bank is, to our knowledge, the first peer\-reviewed system evaluated under the exact Wu et al\. rubric\.

## Appendix ABKimi K2\.5 Cross\-Generator Validation

Model\.Kimi K2\.5 \(kimi\-k2\.5\), released January 2026 by Moonshot AI\. 1T MoE with 32B active parameters, 256K context, Modified MIT License\.

Configuration\.Temperature 1\.0 \(Moonshot default\)\. Max tokens 1500 \(re\-run from initial 500 to avoid reasoning clipping\)\.

Table 53:Cross\-generator validation: GPT\-5\.4 vs Kimi K2\.5\. The lower block lists the additional A\-MEM and Mem0 \(gpt\-4\.1\-mini\) configurations introduced in §[6](https://arxiv.org/html/2609.10413#S6)\.*Correction:*three cells of the A\-MEM \(GPT\-5\.4\) row were transcription errors in the submitted version \(Partial19\.019\.0, Wrong20\.020\.0, Abstain42\.242\.2\); recomputed from the raw per\-question judgments \(n=516n=516\) they are27\.527\.5\(142142\),28\.328\.3\(146146\) and25\.425\.4\(131131\)\. The printed Correct \(18\.8%18\.8\\%,9797\), Confab \(47\.0%47\.0\\%\) and Safe \(44\.2%44\.2\\%\) cells were already correct—indeed the printed Correct and Safe cells force Abstain=25\.4%=25\.4\\%—so no gap, ranking or downstream figure changes \(Appendix[AI](https://arxiv.org/html/2609.10413#A35)\)\.SystemGeneratorCorrectPartialWrongAbstainConfabSafeFR\-BankGPT\-5\.431\.2%17\.4%9\.3%42\.1%22\.4%73\.3%FR\-BankKimi K2\.533\.1%23\.0%16\.0%27\.9%26\.1%61\.0%FR\-GraphitiGPT\-5\.422\.9%20\.3%12\.8%44\.0%23\.9%66\.9%FR\-GraphitiKimi K2\.529\.6%24\.4%16\.4%29\.6%26\.9%59\.2%Memory\-R1GPT\-5\.419\.6%25\.2%16\.7%38\.6%31\.5%58\.1%Memory\-R1Kimi K2\.526\.4%27\.2%21\.5%24\.9%37\.3%51\.3%Mem0GPT\-5\.418\.6%28\.5%24\.2%28\.7%45\.1%47\.3%Mem0Kimi K2\.524\.5%31\.4%28\.5%15\.7%44\.4%40\.2%A\-MEMGPT\-5\.418\.8%27\.5%28\.3%25\.4%47\.0%44\.2%A\-MEMKimi K2\.515\.9%22\.0%24\.6%37\.5%25\.9%53\.4%Mem0 \(gpt\-4\.1\-mini\)GPT\-5\.427\.3%23\.1%24\.8%24\.8%33\.8%52\.1%Mem0 \(gpt\-4\.1\-mini\)Kimi K2\.517\.1%27\.5%48\.5%6\.9%17\.1%24\.0%

The rank order FR\-Bank<<FR\-Graphiti<<Memory\-R1<<Mem0 is identical across generators\. The tier\-average gap between lifecycle\-managed and unmanaged systems is∼\{\\sim\}15pp on both generators \(15\.1pp on GPT\-5\.4, 14\.4pp on Kimi K2\.5\)\. Kimi is systematically∼\{\\sim\}10pp less safe due to a stronger preference for answering over abstaining\. Because Kimi K2\.5 was evaluated at its default temperature \(1\.0\) rather than temperature 0, this cross\-generator comparison constitutes a stress test under realistic deployment settings rather than a controlled same\-temperature replication; the preservation of rank ordering despite this additional source of variance strengthens the generator\-independence finding\.

Behavioral difference\.Kimi K2\.5 systematically prefers answering over abstaining: correct rate increases by \+1\.9 to \+6\.8pp across all systems while abstain rate decreases by 13\.0 to 14\.4pp\. The abstention drop is much larger than the correct\-rate gain because most of the extra answering capacity converts into wrong answers\. This is a uniform behavioral shift, and the relative hierarchy is preserved\.

This rules out three potential confounds: \(a\) GPT\-5\.4\-specific quirks driving the result, \(b\) shared OpenAI training data biases, \(c\) self\-preference effects from generator\-judge alignment\. Retrieval context quality determines downstream response quality independent of the generator\.

Methodology\.For each of 516 questions across 4 systems, the same retrieved top\-10 facts used in the GPT\-5\.4 evaluation were fed to Kimi K2\.5 \(hosted via Moonshot’s API athttps://api\.moonshot\.ai/v1\)\. Persona\-name resolution was added to the prompt\. The same Claude Sonnet judge evaluated both generators\. Total Kimi K2\.5 API cost for 2,064 generations: under $10\.

Recovery of Mem0 E2E data\.The original Mem0 E2E results were spread across three git commits and partially overwritten\. The complete merged dataset was reconstructed for the cross\-generator validation\.

### AB\.1Full Per\-Attack\-Vector Breakdown \(Kimi K2\.5\)

Table 54:Full per\-AV E2E on Kimi K2\.5 across all five systems\.FR\-BankFR\-GraphitiMemoryOSMemory\-R1Mem0AVnnCorrConfCorrConfCorrConfCorrConfCorrConfAV17551\.46\.147\.819\.617\.331\.750\.718\.834\.359\.7AV27519\.744\.15\.643\.84\.043\.27\.061\.07\.066\.1AV39432\.314\.618\.618\.819\.114\.032\.618\.331\.510\.5AV44455\.815\.655\.019\.420\.521\.134\.125\.936\.647\.2AV5402\.744\.10\.044\.40\.029\.60\.048\.60\.040\.6AV6452\.271\.90\.072\.72\.252\.27\.165\.49\.860\.5AV74038\.930\.828\.935\.07\.550\.02\.995\.05\.987\.9AV86363\.510\.079\.73\.828\.68\.749\.26\.152\.514\.6AV94010\.038\.922\.220\.012\.523\.527\.041\.421\.625\.0All51633\.126\.129\.626\.913\.629\.226\.437\.324\.544\.4

On AV7, the hierarchy replicates: FR\-Bank 30\.8%<<FR\-Graphiti 35\.0%<<MemoryOS 50\.0%<<Mem0 87\.9%<<Memory\-R1 95\.0%, matching the GPT\-5\.4 ordering\. Lifecycle\-managed systems sit at<<36% AV7 confabulation on both generators and unmanaged systems at\>\>85% on both; the\>\>50pp tier gap is preserved\. On AV1, FR\-Bank reaches 51\.4% correct with 6\.1% confabulation versus Mem0’s 34\.3%/59\.7%—a nearly10×10\\timesconfab gap\. On AV2 the correct\-rate gap is even sharper: FR\-Bank 19\.7% versus the next\-best 7\.0%, a2\.8×2\.8\\timeslead driven by event\-time expiry filtering\.

MemoryOS on Kimi: generator\-dependent confab reduction, but the retrieval\-metric paradox persists\.On GPT\-5\.4, MemoryOS sits at 40\.8% confabulation\. On Kimi K2\.5, MemoryOS drops to 29\.2%—an 11\.6pp reduction concentrating on AV2 \(67\.5%→\\to43\.2%\), AV7 \(81\.2%→\\to50\.0%\), and AV1 \(43\.2%→\\to31\.7%\)\. Manual inspection suggests Kimi is more willing to hedge when presented with generic summaries\. Critically, the correct rate remains essentially unchanged \(13\.2% GPT\-5\.4→\\to13\.6% Kimi\): hedging converts confabulations into abstentions but does not recover specific answers from information\-destroyed contexts\.

The AV2 inversion between generators\.On AV2, GPT\-5\.4 ranks Memory\-R1 \(61\.2%\) as slightly less confabulatory than Mem0 \(67\.3%\); Kimi preserves that direction\. FR\-Bank remains highest on correct rate on both generators, and MemoryOS edges out FR\-Bank on confab by a narrow 0\.9pp on Kimi—close enough that the result is within noise\.

The AV9 divergence on Kimi\.FR\-Bank achieves 10\.0% correct on AV9 on Kimi versus Memory\-R1’s 27\.0%—the worst correct rate among the five systems\. The mechanism is Kimi’s stronger preference for answering over abstaining interacting unfavorably with FR\-Bank’s soft\-supersession policy: when both values remain in the retrieval set, Kimi selects one and commits\. FR\-Graphiti’s entity\-level resolution avoids this exposure\. This is a genuine limitation of soft supersession under high\-commitment generators\.

Methodological note\.Initial evaluation at max\_tokens=500 clipped Kimi’s reasoning on harder questions, returning empty responses withfinish\_reason=length\. Re\-run at max\_tokens=1500 shifted all systems’ confabulation uniformly by \+3–7pp \(harder questions now included\)\. Rank order preserved exactly\. The uniform shift is evidence that the dropout bias was a measurement artifact affecting all systems similarly\.

## Appendix ACExtended Discussion

The main\-body discussion is condensed\. The following paragraphs provide the full analysis\. The first four paragraphs were moved from §[7](https://arxiv.org/html/2609.10413#S7)to honor the 9\-page main\-body limit; the remaining material extends the limitations and methodology notes that remain in the main body\.

The behavioral ontology was discovered, not designed\.The identity gravity well forced the three\-way split into Identity, Hobbies, and Preferences\. The classify\-the\-fact\-not\-utterance principle emerged from systematic classification failures\. Rate calibration squatting was found through ablation\. The result is an empirically grounded, interpretable framework where the ontology is the prior and per\-user evolution is the posterior\. Memory\-R1’s learnedDELETEproduces 90% AV7 confabulation, identical to Mem0’s 91\.4%, because the action vocabulary lacks retraction as a primitive: optimization cannot induce an action that does not exist\.

Staleness is conditional on retrieval recall, not absolute\.FR\-Graphiti reaches75%75\\%Hit@5 with8%8\\%staleness; FR\-Bank reaches97%97\\%Hit@5 with15\.5%15\.5\\%staleness\. FR\-Bank still leads overall pass and matches on E2E confabulation, because at high recall the correct fact almost always coexists with stale ones in the retrieval set and the downstream LLM can resolve the contradiction\. Staleness becomes catastrophic only when recall is low and the stale fact is the only signal available, which is the regime in which Mem0 confabulates 91\.4% on AV7\. Substrate choice trades supersession precision against retrieval recall without altering the policy layer\.

Retrieval metrics can misdiagnose lifecycle quality\.Standard memory benchmarks measure whether the correct fact appears in the top\-KK, implicitly assuming that correct system behavior is always*presence*\. For retraction, expiry, and supersession, the correct behavior is*absence*\. On AV7, FR\-Bank achieves 5% retrieval pass but 37\.5% end\-to\-end correctness, the highest of any evaluated system, while MemoryOS scores 57% retrieval pass but only 7\.5% correct, because hierarchical summarization produces generic content that passes retrieval by containing nothing specific to be wrong about\. The full AV7 breakdown for FR\-Bank is37\.5%37\.5\\%correct,32\.5%32\.5\\%abstain,7\.5%7\.5\\%wrong,22\.5%22\.5\\%confabulated; the system’s advantage lies primarily in converting confabulations into abstentions rather than producing correct answers, and the100%100\\%extraction\-missing failure rate on AV7 \(Appendix[D](https://arxiv.org/html/2609.10413#A4)\) identifies extraction quality as the binding constraint\. Future memory system evaluations must pair retrieval metrics with end\-to\-end response quality\.

Methodology integrity for LongMemEval comparisons\.Future LongMemEval comparisons should hold the Wu et al\. judge protocol fixed; results obtained under different judges or prompts should be reported separately and not benchmarked against canonical numbers\. Holding the rubric constant is a service to the community, not self\-promotion\.

The LifecycleBench result validates the thesis—through precision, not recall\.At 40\-persona scale, FR achieves 73% pass with 8% staleness versus baseline’s 61%/18%\. The 4\-config ablation cleanly decomposes contributions\. Five\-phase scaling validation \(8→\\to40 personas\) confirms gains are stable\.

End\-to\-end evaluation closes the causal loop\.The retrieval\-to\-response chain is now empirically validated: lifecycle management→\\tocleaner context→\\tofewer confabulations\. The confabulation gap \(−\-22\.7pp over answered queries,−\-19\.2pp over all queries\) is larger than the pass rate gap \(\+16pp\), confirming that lifecycle management’s primary value is preventing wrong answers, not just finding right ones\. The safe response rate \(correct\+\+abstain\) captures this: FR\-Bank 73\.3% and FR\-Graphiti 66\.9%, against Mem0’s 47\.3%\. Both FR variants produce responses that do not mislead users on roughly two\-thirds or more of queries\.

Cross\-system comparison confirms the thesis at the field level\.Against Mem0, Memory\-R1, and MemoryOS—representing flat vector stores, RL\-learned operations, and cognitive hierarchies—FR\-Bank achieves the highest pass rate \(76\.9%\) and lowest confabulation \(22\.4%\)\. The five\-system comparison reveals a clean hierarchy: no lifecycle management \(Mem0\)<<learned operations \(Memory\-R1\)<<cognitive hierarchy \(MemoryOS\)<<designed lifecycle policies \(FR\-Bank\)\. MemoryOS’s competitive retrieval metrics \(70\.5% pass\) mask a downstream failure: only 13\.2% correct rate, confirming that cognitive ontologies do not preserve fact\-level granularity\.

The retrieval metric paradox reveals a methodological gap\.Standard evaluations do not measure whether useful facts are also present\. A system producing vague summaries can pass retrieval evaluations by having nothing specific to be wrong about\. MemoryOS provides an empirical demonstration: 96% of its AV7 “passes” and 91% of its AV6 “passes” are information\-loss artifacts\. We argue that future memory system evaluations must include end\-to\-end response quality alongside retrieval metrics; retrieval\-level evaluation alone is vulnerable to inflation by lossy compression\.

Positional staleness reveals a hidden failure mode\.Aggregate staleness rates understate downstream impact\. Mem0 places stale facts at rank 1 \(8×8\\timesFR’s rate\), causing the LLM to anchor responses on outdated information\. On AV7, 90% of queries have retracted plans in high\-attention positions\.

Composability is empirically validated\.Supplementary identity/health extraction halved the AV3 gap without any lifecycle changes\. The ontology serves dual purposes: lifecycle management and retrieval organization \(category\-forced retrieval recovered \+6pp on AV3 with zero regressions\)\.

Substrate independence validates the policy contribution\.The lifecycle layer achieves comparable results on two fundamentally different substrates: a temporal knowledge graph \(Graphiti, 73% pass, 8% staleness\) and a flat embedding bank \(FR\-Bank, 76\.9% pass, 15\.5% staleness\)\. The same parameters applied to completely different storage backends produce consistent lifecycle gains\.

Cross\-generator validation strengthens the architectural gap claim\.The replication on Kimi K2\.5 demonstrates that the∼\{\\sim\}20pp gap between lifecycle\-managed and unmanaged retrieval is invariant to generator model choice\. Two frontier models from independent labs, trained on different data with different weight regimes, produce nearly identical confabulation hierarchies\.

Evaluation protocol determines reported performance\.Independent evaluation by Pollertlam & Kornsuwannawit\[[18](https://arxiv.org/html/2609.10413#bib.bib18)\]reports Mem0 at 49\.0% on LongMemEval with GPT\-4o, substantially below Mem0’s self\-reported numbers\. APEX\-MEM\[[17](https://arxiv.org/html/2609.10413#bib.bib17)\]reports 86\.2% with Claude Sonnet as the QnA agent but 75\.0% with GPT\-4o—an 11\.2pp swing from the answerer model alone\. FR\-Bank reports 75\.2% under the original Wu et al\. protocol with gpt\-4o\-mini as the answerer, the weakest model in any published comparison\. An answerer\-model ablation substituting gpt\-4o for gpt\-4o\-mini yields 73\.6% \(−\-1\.6pp, within run\-to\-run variance\), confirming that retrieval context quality, not answer\-generator capability, is the binding constraint\.

Cross\-benchmark validation on LongMemEval\.FR\-Bank scores 75\.2% on the full 500\-question LongMemEval\-S canonical benchmark under the exact Wu et al\. \(ICLR 2025\) judge protocol—to our knowledge the first peer\-reviewable result that holds the Wu et al\. rubric fixed, and∼\+5\{\\sim\}\+5pp above the closest peer\-reviewed reference \(RMM, ACL 2025, 70\.4%; see Appendix[AA](https://arxiv.org/html/2609.10413#A27)for the generator/judge mismatch caveats\)\. The same FR\-Bank configuration also reaches 79\.5% on the 234\-question oracle POC subset \(\+8\.3pp over Zep/Graphiti’s 71\.2%\[[2](https://arxiv.org/html/2609.10413#bib.bib2)\], arXiv preprint\), with a no\-lifecycle ablation isolating \+7\.4pp to the retrieval pipeline\. The knowledge\-update figure reported in the submitted version \(87\.2% vs 80\.8%,\+6\.4\+6\.4pp\) is withdrawn: it traces to no surviving artifact, and the artifact\-backed value on the 317\-question matched subset is−6\.4\-6\.4pp, a judge\-criterion artifact rather than a lifecycle gain \(Table[21](https://arxiv.org/html/2609.10413#A4.T21), Appendix[AI](https://arxiv.org/html/2609.10413#A35)\)\. All numbers use identical lifecycle parameters—no benchmark\-specific tuning\.

Per\-question banks are the LongMemEval and LoCoMo standard, not an FR\-Bank concession\.Both LongMemEval\[[1](https://arxiv.org/html/2609.10413#bib.bib1)\]and LoCoMo\[[13](https://arxiv.org/html/2609.10413#bib.bib13)\]score each question against its associated conversation haystack rather than against a single persistent memory store; FR\-Bank follows this oracle protocol directly, which is why the 75\.2%/79\.5% numbers are comparable to Wu et al\. \(ICLR 2025\), RMM \(ACL 2025\), and the Zep/Graphiti arXiv report\. The regime that stresses a fully persistent store accumulating thousands of conversations is precisely what LifecycleBench measures \(one bank per persona,∼\{\\sim\}35 multi\-session conversations, 516 lifecycle\-sensitive queries against the same bank\), and FR\-Bank’s 76\.9% pass and 15\.5% staleness in that regime is the datapoint that governs deployed\-store behavior\. The two benchmarks therefore play complementary roles: LongMemEval/LoCoMo measure retrieval under the community\-standard oracle haystack, and LifecycleBench measures lifecycle dynamics under a persistent per\-persona store\.

Complementarity with existing approaches\.Memory\-R1’s RL\-trained operations achieve strong retrieval quality \(MRR 0\.816\) but lack structural mechanisms for event\-time expiry and retraction\. Our ontology could serve as initialization, reward shaping, or structural constraint for RL\-based managers\. FluxMem’s adaptive structure selection is orthogonal and could compose with behavioral lifecycle policy\.

Benchmark saturation motivates lifecycle evaluation\.LongMemEval has been effectively solved at approximately 95% accuracy by practitioners\. Yet it does not measure staleness, supersession, expiry, retraction, or any temporal state management capability\. LifecycleBench fills this gap with 9 attack vectors targeting failure modes invisible to existing benchmarks\.

### AC\.1Privacy, Consent, and Safety

Memory systems that retain personal facts raise privacy and safety concerns beyond those addressed in this work\. Deployed systems require explicit user consent for memory retention, verifiable deletion guarantees when users request removal, and safeguards against memory poisoning through adversarial conversational inputs\. The current ingestion classifier detects instructional content \(Appendix[B](https://arxiv.org/html/2609.10413#A2)\), but production deployment would require substantially stronger prompt\-injection defenses\. Incorrect persistence in sensitive categories, particularly Health and Financial, could cause real harm; the interpretability of FR’s category labels and lifecycle policies provides a foundation for user\-facing memory controls, but we do not evaluate user\-facing interfaces in this work\. Finally, the decay rates and supersession semantics encode assumptions about how personal facts change over time that may not generalize across cultural contexts; per\-user parameter adaptation \(Appendix[B](https://arxiv.org/html/2609.10413#A2)\) is designed to address this but remains unvalidated\.

### AC\.2Introduction: Extended Motivation

The following material provides extended motivation from the introduction\.

Real memory is not a queue; it is a graph with activation patterns\. The question is not only how to find the right context, but how to determine which memories should persist, which should be replaced, which should expire, and at what rate—conditioned on the type of memory\.

Consider a user interacting three times per day over two years, producing 10,000–30,000 facts\. At retrieval time: three “works at” facts coexist with equal status; a six\-month\-old dentist appointment still scores highly on queries about upcoming plans; ADHD mentioned once in session 3 is buried under thousands of more recent edges; an explicit retraction \(“forget about the Denver move”\) competes with the original plan; and “thinking about moving to London” is treated as contradicting “I live in Istanbul\.” The downstream LLM sees all facts as equally valid and either hallucinates a synthesis or picks arbitrarily\.

We introduce Fortunate Recall: not total recall, but intelligent recall\. The system forgets according to the behavioral type of each fact—structured, adaptive persistence where unchecked forgetting would otherwise erode coherence\.

## Appendix ADPre\-Registered Untyped Lifecycle Baseline

This appendix gives the design, protocol, and full results for the ablation summarized in §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)\.

### AD\.1Pre\-Registration

Three documents fix the design before data contact\. The first registers the three\-primitive arm itself, defining the rules verbatim—“supersede==latest\-slot\-wins; expire==date rule; retract==drop entries withis\_retracted = True\. No category routing, no soft blending, no decay, no ontology\.” The second is an amendment resolving a dataset\-scope ambiguity, ruled on before any run\. The third registers the end\-to\-end comparison reported here, including the analysis branch table: which contrast would be treated as primary was fixed in advance under each possible outcome, so the reported branch was not selected after seeing the data\. Commit hashes for all three, and the raw retrieval, generation, and judging outputs, are in the released artifacts\.

### AD\.2What the Arm Is, Exactly

The arm is more austere than the phrase “typed versus untyped” suggests, and we state the gap rather than let it be inferred\. It retains slot\-key supersession, event\-time expiry, and the retraction\-state mask\. It removes not only the behavioral categories but also activation, decay, and score blending: candidates are ranked by*semantic similarity alone*over an unmasked cosine\+\+BM25 pool, with no category routing, no category\-forced retrieval, and no multi\-hop expansion\. Two further deltas are disclosed for completeness: its expiry rule carries no numeric exemption, and its retraction mask is applied unconditionally, whereas canonical FR gates the mask behind a retraction\-query detector\. The consequence for interpretation is that this arm*lower\-bounds*a lifecycle\-metadata\-only system rather than isolating the category labels as a single variable—and that direction of error strengthens rather than weakens the reading we draw from it, because a baseline weaker than advertised still ties on correctness\.

### AD\.3Protocol and Results

Both arms’ top\-10 contexts were answered by the same GPT\-5\.4 generator \(temperature 0\) on all 516 LifecycleBench questions and scored by a single pinned judge under the end\-to\-end rubric of Appendix[N](https://arxiv.org/html/2609.10413#A14), in one judging pass as the pre\-registration requires\.

Table 55:Full stack versus the untyped three\-primitive arm,n=516n=516, single paired judging pass\. Confabulation is over all queries\. McNemarbbcounts questions where only the full stack shows the outcome andccwhere only the untyped arm does\.MeasureFull FR\-BankUntyped armΔ\\Delta\(95% CI\)McNemarCorrect / total26\.9%28\.7%−1\.7\-1\.7pp\[−6\.0,\+2\.7\]\[\-6\.0,\+2\.7\]b=50b\{=\}50,c=59c\{=\}59,p=0\.44p=0\.44Confabulation / all12\.0% \(62\)24\.2% \(125\)−12\.2\-12\.2pp\[−16\.1,−8\.2\]\[\-16\.1,\-8\.2\]b=21b\{=\}21,c=84c\{=\}84,p<0\.001p<0\.001Abstention\+15\.9\+15\.9pp for the typed stack——The correctness contrast is null and the confabulation contrast is large and one\-sided: 84 questions are confabulated only by the untyped arm against 21 only by the full stack\. Since correct\-over\-total does not move while abstention rises15\.915\.9pp, the additional abstentions are drawn from would\-be wrong or fabricated answers rather than from correct ones—the “identical behavior on answered questions” hypothesis, tested and rejected within a single pipeline\.

### AD\.4Judge\-Pass Provenance

The pre\-registration requires both arms in one pass, so this pass re\-judged the original FR\-Bank answers rather than regenerating them; the answer strings are byte\-identical on 516/516 questions\. The pass uses the same judge model and a byte\-identical rubric through a different access path\. FR\-Bank’s all\-queries confabulation is13\.0%13\.0\\%\(67/51667/516; 68 raw, with oneabstain\-flagged record zeroed under the rubric’s abstain rule\) under the original pass and12\.0%12\.0\\%\(62/51662/516\) under the paired pass—a five\-question difference produced by 16 confabulation\-flag flips on identical answers \(11 to clean, 5 to confabulated\), against89\.1%89\.1\\%verdict\-class agreement between the passes overall\. This is the judge\-relative variability characterized in Appendix[AG](https://arxiv.org/html/2609.10413#A33)\. Neither pass supersedes the other\. Every contrast in Table[55](https://arxiv.org/html/2609.10413#A30.T55)is computed entirely within the paired pass and is unaffected by the choice\.

## Appendix AEExternal Transfer: BEAM

### AE\.1The Benchmark, and Why It Answers the Co\-Design Objection

BEAM\[[14](https://arxiv.org/html/2609.10413#bib.bib14)\]contains 100 coherent conversations and exactly 2,000 probing questions—two per conversation for each of ten memory abilities—across context tiers from 128K to 10M tokens\. It was constructed independently of this work and is human\-validated\. Three of its abilities \(contradiction resolution, event ordering, instruction following\) were newly introduced by its authors, so they cannot derive from FR’s design or from the baseline failure modes that informed LifecycleBench’s attack vectors\. We restrict to the five lifecycle\-relevant abilities at the 1M\-token tier \(n=70n=70per ability\), which was pre\-registered together with the FR\-vs\-Mem0 comparison before data contact; the ontology\-collapse arm and the granularity sweep are follow\-up analyses under the same design\.

### AE\.2Standing Disclosures

Two disclosures bind every number in this appendix and in §[6\.6](https://arxiv.org/html/2609.10413#S6.SS6)\.

Backbone quarantine\.These runs use a different generator backbone from the canonical LifecycleBench evaluation\. The arms are internally comparable to one another under an identical harness, but the absolute values are*not*commensurable with the LifecycleBench tables elsewhere in this paper, and we do not pool them\.

Judge asymmetry\.The judge used here has perfect abstention recall \(15/1515/15on a bridge sample against our frozen API judge\) but over\-abstains relative to it \(precision15/1815/18\)\. Confabulation counts are therefore lower bounds and abstention rates upper bounds—uniformly across all arms, so comparisons between arms are unaffected while absolute levels are not directly comparable to the LifecycleBench numbers\.

### AE\.3Replication and Spread

The primary configuration was measured three times under the same judge and backbone\. Reporting the primary result without this block would overstate its precision\.

Table 56:Three independent executions of the identical FR\-full configuration, plus the two independently specified minimal arms\. The prompt cache was reaped between runs, so each is a genuine re\-generation\.RunBinary / 280CRKUTRAbstConfabFR\-full, primary1312933264372FR\-full, run 21282533313979FR\-full, run 31252833253975Minimal arm A \(k=1k\{=\}1collapse\)1181934244184Minimal arm B \(untyped defaults\)1151931224376Mem0925341538108Lifecycle\-off1352443264284FR\-full spans125125–131131of 280 \(six questions,2\.12\.1pp\) on an identical configuration, with knowledge update at 33 in all three runs\. This is generator and judge noise on one harness, and it is why §[6\.6](https://arxiv.org/html/2609.10413#S6.SS6)quotes the ontology effect as a range \(\+10\+10to\+13\+13\) rather than a point estimate, and the metadata component as\+23\+23to\+26\+26\. Minimal arms A and B are different specifications with different pool construction—A collapses the eleven cells to one with global\-meanλ\\lambda/α\\alpha/floor, B replaces every category lookup with untyped defaults \(λ=0\.005\\lambda=0\.005,α=0\.20\\alpha=0\.20, floor0\.00\.0\) and removes the category\-forced pool—and both land on exactly19/7019/70contradiction resolution\. Neither is the LifecycleBench arm of Appendix[AD](https://arxiv.org/html/2609.10413#A30), which keeps none of the uniform decay, blending, multi\-hop, or intent routing that these two retain\.

### AE\.4Honest Negatives

The confabulation decomposition does not replicate\.The primary run falls monotonically108→84→72108\\to 84\\to 72, but on re\-execution the two FR arms are indistinguishable \(7676vs\.7575\)\. The Mem0→\\toFR drop is robust; the minimal→\\tofull drop is not independently replicated and must be read as unreplicated\. The correctness half of the decomposition does replicate\.

Lifecycle\-off scores highest overall\.At135/280135/280it beats both typed arms, driven by knowledge update4343vs\.3333\. Pairing on\(conversation, question\)gives 12 discordant knowledge\-update questions against 2 in the other direction, a net cost of 10\. In 10 of those 12, ingest\-time supersession fired under an over\-broad slot key and deactivated the entry carrying the current value, emptying the candidate pool entirely in 7\. Median slot cardinality among the offending keys is 7 \(maximum 67\)\. A cardinality guard exists but was default\-off and, at its configured threshold, would have fired on only 2 of the 13 offending deactivations, so it is not the remedy; slot\-key granularity retuning is, and it is identified in the released analysis\. The minimal arm inherits the same cost \(knowledge update 31\), which is what locates the cost in the generic primitives rather than in the ontology\.

Event ordering is at the floor\.Exact\-correct is0/700/70for every arm\. Our frozen judge has no ordering rubric and initially returned 0/70 with spurious confabulation flags for all three arms symmetrically \(68, 68, 69 flags\); a hand\-scoring audit identified this as a scorer artifact, and the decision to rescore under BEAM’s official graded scorer and exclude the ability from the binary aggregate was taken on that diagnostic evidence before its aggregate effect was computed\. Under the official scorer,τnorm\\tau\_\{\\text\{norm\}\}is0\.21360\.2136/0\.21120\.2112/0\.19000\.1900andllm\_judgeis0\.5740\.574/0\.5860\.586/0\.5100\.510for FR\-full / minimal / Mem0; FR\-vs\-Mem0 is significant on both \(Wilcoxon signed\-rank,n=70n=70:p=0\.009p=0\.009andp=0\.020p=0\.020\) while FR\-full vs\. FR\-minimal is not \(p=0\.67p=0\.67andp=0\.19p=0\.19\), consistent with event ordering being ontology\-independent\. Hand\-scores, per\-question official scores, and the verbatim\-reproduction log are released\.

### AE\.5Provenance

Every number above is counted directly from per\-question judge records rather than transcribed from any response document: per\-abilityjudge\_k1\.jsonl/judge\_k11\.jsonlfiles for the ablation arms,onto\_sweep\_k\{3,5,7,9\}/judge\.jsonlfor the granularity sweep, and a single combined judgments file for the Mem0, lifecycle\-off, and re\-run arms\. Correct counts arecorrectness == "CORRECT"; confabulation counts sum the judge’s confabulation flag\. The released manifest gives one line per number in §[6\.6](https://arxiv.org/html/2609.10413#S6.SS6)and this appendix, naming the file and the operation that produces it, together with a SHA\-256 for each raw file\.

## Appendix AFAll\-Queries End\-to\-End Metrics

Reviewers correctly observed that confabulation over non\-abstaining responses flatters systems that abstain often\. Table[57](https://arxiv.org/html/2609.10413#A32.T57)recomputes every end\-to\-end rate over all 516 queries from the raw per\-question judgments\. Convention, stated because more than one is defensible: anabstainis never counted as a confabulation, the “all queries” denominator is all 516 questions, and the “answered” denominator excludes abstentions only\.

Table 57:End\-to\-end response quality under both denominators,n=516n=516, GPT\-5\.4 generator\. Safe==correct\+\+abstain\.SystemCorrect / totalAbstainConfab / allConfab / answeredSafeFR\-Bank31\.2%42\.1%13\.0%22\.4%73\.3%FR\-Graphiti22\.9%44\.0%13\.4%23\.9%66\.9%MemoryOS13\.2%54\.8%18\.4%40\.8%68\.0%Memory\-R119\.6%38\.6%19\.4%31\.5%58\.2%Mem0 \(gpt\-4\.1\-mini\)27\.3%24\.8%25\.4%33\.8%52\.1%Mem0 \(default\)18\.6%28\.7%32\.2%45\.1%47\.3%A\-MEM18\.8%25\.4%35\.1%47\.0%44\.2%Three observations\. First,19\.219\.2of the22\.722\.7pp FR\-Bank – Mem0 gap survives the denominator change\. Second, correct\-over\-total favors FR\-Bank by12\.612\.6pp \(31\.2%31\.2\\%vs\.18\.6%18\.6\\%\), so abstention is not substituting for correctness\. Third, the ranking is essentially stable; the one movement is MemoryOS, whose low all\-queries confabulation pairs the highest abstain rate with the lowest correct rate—the retrieval\-metric paradox of Appendix[D](https://arxiv.org/html/2609.10413#A4), not a lifecycle success\.

The A\-MEM row here is the recomputed one\. The submitted version’s Table[53](https://arxiv.org/html/2609.10413#A28.T53)printed Partial19\.019\.0, Wrong20\.020\.0and Abstain42\.242\.2for A\-MEM on GPT\-5\.4; those three cells were transcription errors, detectable from the row itself because the printed Correct \(18\.8%18\.8\\%\) and Safe \(44\.2%44\.2\\%\) cells force Abstain=25\.4%=25\.4\\%\. Recomputed from the raw judgments the row is Correct18\.8%18\.8\\%\(97\), Partial27\.5%27\.5\\%\(142\), Wrong28\.3%28\.3\\%\(146\), Abstain25\.4%25\.4\\%\(131\), summing to 516\. Correct, Confab and Safe were already right, so no gap, ranking, or downstream figure changes\.

## Appendix AGValidation of the End\-to\-End Judge

Every verdict in this paper is produced by an LLM judge, so we audited that judge with two independent machine instruments before claiming anything from its output\. Both were pre\-registered with explicit predictions; three of the four predictions were refuted, and we release them alongside the results\.

### AG\.1Six\-Model Cross\-Family Panel

One hundred stratified verdicts were re\-judged by six models spanning five model families, each receiving a byte\-identical rubric and the ground\-truth evidence, in fresh sessions with memory disabled\. The panel agrees with itself substantially more than with our pinned judge: Fleissκ=0\.834\\kappa=0\.834across the six panelists and0\.7960\.796across all seven raters, with a median pairwiseκ\\kappaof0\.8140\.814among panelists but0\.7150\.715between panelists and the pinned judge\. Fifteen of the 21 pairs fall outside\[0\.60,0\.75\]\[0\.60,0\.75\]\.

The disagreement is not diffuse but localized\. Against the panel majority, the pinned judge’scorrect,wrongandabstainverdicts are stable \(23/24, 19/20 and 32/32 respectively\), while of 24 pinnedpartialverdicts the panel majority moves 19 elsewhere—13 tocorrectand 6 toabstain\. Inspection of those 19 shows none contains an outdated or wrong indicator; all 19 are merely*incomplete*\. The pinned judge is therefore usingpartialto mean “incomplete” where our rubric reserves it for “contaminated\.” One item is a 3–3 tie with no panel majority and is reported as its own case rather than folded into an agreement tier\.

### AG\.2Targeted Re\-Judge of Every PARTIAL Verdict

Acting on that diagnosis, all 748 pinnedpartialverdicts across six systems were re\-judged by an independent judge under the same rubric, together with a 60\-item stratified control of non\-partialverdicts\. MemoryOS is excluded because its answer texts were not persisted\.

The control reproduces56/6056/60\(93%93\\%\) of non\-partialverdicts—95%95\\%ofcorrect,85%85\\%ofwrong,100%100\\%ofabstain—which is what licenses correctingpartialalone\. Applying the corrections raises correct rates by\+5\.2\+5\.2to\+7\.0\+7\.0pp across the six systems, roughly uniformly: FR\-Bank31\.2→36\.2%31\.2\\to 36\.2\\%, FR\-Graphiti22\.9→28\.1%22\.9\\to 28\.1\\%, Mem018\.6→25\.2%18\.6\\to 25\.2\\%, Mem0\-mini27\.3→34\.3%27\.3\\to 34\.3\\%, Memory\-R119\.6→24\.8%19\.6\\to 24\.8\\%, A\-MEM18\.8→24\.8%18\.8\\to 24\.8\\%\. The cross\-system ranking is unchanged on every metric, and the FR\-Bank – Mem0 correct\-rate gap narrows from\+12\.6\+12\.6to\+11\.0\+11\.0pp\.

Two caveats travel with this\. The all\-queries confabulation baseline computed inside the re\-judge harness differs slightly from Table[57](https://arxiv.org/html/2609.10413#A32.T57)\(e\.g\. FR\-Bank13\.2%13\.2\\%vs\.13\.0%13\.0\\%\) because the two harnesses treat the confabulation flag on re\-scored items differently; the paper’s tables use the convention stated in Appendix[AF](https://arxiv.org/html/2609.10413#A32)throughout\. And the two audits disagree with each other on magnitude: on the 24 items both examined, the panel majority moved 19 offpartialwhile the single independent judge moved 11, a 33pp discrepancy\. They agree on the direction and the location of the bias but not its size, so the panel’s item\-level agreement figures should not be quoted as a general property of the judge\.

### AG\.3What Remains

The pinned\-judge numbers remain the numbers of record throughout this paper, because they are the ones every system was scored under identically\. What the audits establish is that absolute rates are judge\-relative and cross\-system comparisons are robust\. A stratified human\-labeled slice—100 verdicts across the four verdict classes and nine attack vectors, two non\-author annotators blind to system identity, reporting raw agreement, Cohen’sκ\\kappa, and a per\-class confusion table, prioritizing items on which the machine judges disagree—is planned and has not yet been run\. It is listed as the first limitation in §[7](https://arxiv.org/html/2609.10413#S7)\.

## Appendix AHMetadata\-Noise Sensitivity Across the Full Basis

The deterministic policy layer is only as reliable as the LLM\-generated metadata beneath it\. Appendix[B\.1\.2](https://arxiv.org/html/2609.10413#A2.SS1.SSS2)perturbs category labels alone; this study perturbs each field of the basis independently\.

Harness and scope\.Noise is injected at ingestion and lifecycle states are recomputed by a state replay verified to reproduceis\_activefor18,936/18,93618\{,\}936/18\{,\}936edges; retrieval is then rerun on all 516 questions\. The0%0\\%\-noise control reproduces the unperturbed top\-10 exactly, and the harness reproduces the published Appendix[B\.1\.2](https://arxiv.org/html/2609.10413#A2.SS1.SSS2)anchors to\|Δ\|<10−5\|\\Delta\|<10^\{\-5\}before any new condition is run\. Two scope limits are declared rather than discovered: category\-forced retrieval, multi\-hop expansion and LLM distillation are excluded because they require API calls, so every row is a*lower bound*on full\-pipeline impact—and the category row is the one most likely understated, since category\-forced retrieval is the component whose input is the category label\. The staleness and support measures are lexical proxies computed against ground\-truth strings, not the LLM judge used for the headline numbers\. Mean±\\pms\.d\. over three seeds\.

Table 58:Retrieval stability under independent metadata corruption\. Jaccard@10 is between the unperturbed and perturbed top\-10 sets;Δ\\Deltastaleness is the change in the fraction of questions whose top\-10 contains an edge the uncorrupted metadata marks superseded, expired, retracted or shadowed \(baseline8\.1%8\.1\\%\)\.Field / sub\-conditionNoise rateJaccard@10Δ\\DeltastalenessCategory label \(full replay\)5%0\.951±0\.0020\.951\\pm 0\.002\+0\.3\+0\.3ppCategory label \(full replay\)10%0\.917±0\.0020\.917\\pm 0\.002\+0\.4\+0\.4ppCategory label \(full replay\)20%0\.854±0\.0060\.854\\pm 0\.006\+1\.4\+1\.4ppCategory label \(full replay\)50%0\.733±0\.0020\.733\\pm 0\.002\+2\.7\+2\.7ppSlot key, merge corruption5%0\.859±0\.0030\.859\\pm 0\.003\+19\.8\+19\.8ppSlot key, merge corruption10%0\.764±0\.004\\mathbf\{0\.764\\pm 0\.004\}\+32\.2\\mathbf\{\+32\.2\}ppSlot key, merge corruption20%0\.650±0\.0020\.650\\pm 0\.002\+52\.7\+52\.7ppSlot key, split corruption5%0\.901±0\.0020\.901\\pm 0\.002\+24\.4\+24\.4ppSlot key, split corruption10%0\.837±0\.005\\mathbf\{0\.837\\pm 0\.005\}\+38\.6\\mathbf\{\+38\.6\}ppSlot key, split corruption20%0\.740±0\.0000\.740\\pm 0\.000\+60\.1\+60\.1ppEvent time,±7\\pm 7\-day shift10%0\.999±0\.0000\.999\\pm 0\.000\+0\.1\+0\.1ppEvent time,±90\\pm 90\-day shift10%0\.998±0\.0010\.998\\pm 0\.001\+0\.3\+0\.3ppEvent time, deleted10%0\.993±0\.0020\.993\\pm 0\.002\+2\.6\+2\.6ppEvent time, deleted20%0\.988±0\.0010\.988\\pm 0\.001\+5\.6\+5\.6ppRetraction, false positive1%0\.971±0\.0030\.971\\pm 0\.003−0\.1\-0\.1ppRetraction, false negative \(all 31 restored\)exhaustive0\.9950\.995\+0\.8\+0\.8ppReading the grid\.Sensitivity concentrates on slot keys—precisely the field that §[6\.5](https://arxiv.org/html/2609.10413#S6.SS5)identifies as carrying correctness—and their corruption damages*set composition*rather than ranking \(Kendallτ≈0\.997\\tau\\approx 0\.997while Jaccard falls to0\.760\.76\)\. Category labels, which carry the calibration benefit, tolerate a 10% uniform flip at\+0\.4\+0\.4pp of staleness and even a 50% flip—equivalent to random assignment within the confused pairs—at\+2\.7\+2\.7pp, with the damage flowing through supersession semantics rather than scoring\. Event\-time anchors are near\-inert under realistic corruption on this corpus because most anchored events lie far from the expiry boundary; only3\.1%3\.1\\%fall within seven days of it\. Retraction states show a prevalence/potency split: per corrupted edge they are the most potent field measured, but only 31 of18,93618\{,\}936edges carry retrieval\-suppressing retraction, so aggregate exposure is minimal\.

The binding constraint on retraction is recall, not noise\.Auditing the corpus against ground truth: the 31 retraction\-carrying edges are detection markers, of which 26 map to the 40 scripted retraction events \(19 distinct events, some firing more than once\) and 5 are incidental\. In event units the ingestion detector fires on19 of 40scripted retractions, so extraction recall on retraction language is the first bottleneck on selective forgetting\. It is not the only one: because a plan is stored across many sibling slot keys, retraction and supersession deactivate the primary key while sibling edges asserting the plan remain active, so only2 of 40events are cleanly suppressed at the metadata level—matching the5%5\\%AV7 retrieval\-pass rate—and 38 of 40 leak at least one live edge\. FR\-Bank’s37\.5%37\.5\\%end\-to\-end AV7 correctness, the highest of any evaluated system, is therefore recovered downstream, where the generator reconciles the co\-retrieved plan and its cancellation, rather than by clean metadata exclusion\. The selective\-forgetting bottleneck is thus twofold—retraction\-detection recall and slot\-key fragmentation—and because the downstream policy is deterministic, both failure modes are localized and inspectable\.

## Appendix AIChanges in This Revision

This appendix lists every number that differs from the submitted version, so that the revision can be audited against it directly\. All corrections were found by our own post\-submission audit or during the recomputations requested in review, and all corrected values are recomputed from raw per\-question records\. Section[6\.5](https://arxiv.org/html/2609.10413#S6.SS5), §[6\.6](https://arxiv.org/html/2609.10413#S6.SS6), §[6\.7](https://arxiv.org/html/2609.10413#S6.SS7), §[6\.7](https://arxiv.org/html/2609.10413#S6.SS7)and Appendices[AD](https://arxiv.org/html/2609.10413#A30)–[AH](https://arxiv.org/html/2609.10413#A34)are new\.

Table 59:Numerical corrections relative to the submitted version\.ItemSubmitted→\\torevisedReasonFR\-Bank LifecycleBench pass rate \(16 sites\)77\.3%→76\.9%77\.3\\%\\to 76\.9\\%, staleness15\.3%→15\.5%15\.3\\%\\to 15\.5\\%The77\.3%77\.3\\%run was superseded by a re\-scored run whose values already underlie every confidence interval and pairwise test in Appendix[D\.6](https://arxiv.org/html/2609.10413#A4.SS6)and the released artifact\. Ranking and every comparative conclusion unchanged; still\+16\+16pp over Mem0\.LongMemEval knowledge\-update\+6\.4\+6\.4pp*withdrawn*The87\.2%87\.2\\%/80\.8%80\.8\\%pair traces to no surviving artifact\. Artifact\-backed value on the 317\-matched subset is−6\.4\-6\.4pp, a judge\-criterion effect \(Table[21](https://arxiv.org/html/2609.10413#A4.T21)\)\.Table[20](https://arxiv.org/html/2609.10413#A4.T20)subset labelnow labeled 234\-question POC subsetThe submitted table mixed a “317\-matched” label with 234\-question POC values; the two subsets are now separate tables\.Table[53](https://arxiv.org/html/2609.10413#A28.T53), A\-MEM \(GPT\-5\.4\) rowPartial19\.0→27\.519\.0\\to 27\.5, Wrong20\.0→28\.320\.0\\to 28\.3, Abstain42\.2→25\.442\.2\\to 25\.4Three transcription errors, forced by the row’s own Correct and Safe cells\. Correct, Confab and Safe were already right; nothing downstream changes\.AV3 leadership \(5 sites\)“Memory\-R1 leads AV3”→\\toFR\-Bank leads at97%97\\%The comparison was against FR\-Graphiti’s78%78\\%\. Memory\-R1 leads no attack vector\.FR MRR0\.478→0\.8300\.478\\to 0\.830where FR\-Bank is meant0\.4780\.478is FR\-Graphiti’s; FR\-Bank’s0\.8300\.830exceeds Memory\-R1’s0\.8160\.816\.Bare “FR” \(5 contradictions\)disambiguated to FR\-Bank / FR\-GraphitiThe same label denoted both variants, producing gaps of up to 35pp between statements about “FR\.”FR\-Graphiti ablation deltas−12\.2/−6\.2/−6\.4→\+12\.2/\+6\.2/\+6\.4\-12\.2/\-6\.2/\-6\.4\\to\+12\.2/\+6\.2/\+6\.4Sign inversion; the per\-AV table already showed positive gains\.Mem0 extractor upgrade\+10\+10pp→\+6\.1\\to\+6\.1pp67\.1−61\.067\.1\-61\.0\.Category\-aware routing\+5\+5pp→\+6\\to\+6ppConsistent with Table[3](https://arxiv.org/html/2609.10413#S6.T3)and the bootstrap estimate\.“2×2\\timeslower staleness”→1\.76×\\to 1\.76\\times15\.515\.5vs\.2727\.Table[44](https://arxiv.org/html/2609.10413#A14.T44)FR and Mem0 columns replaced; all 9 AVs now shownBoth columns matched no current run; the Memory\-R1 column was already correct\.Table[43](https://arxiv.org/html/2609.10413#A14.T43)per\-AV Correct cells replacedThey did not weight\-average to their own \(correct\) aggregates\.AV7 confabulation prose“FR reduces this to32\.5%32\.5\\%”→33\.3%\\to 33\.3\\%32\.5%32\.5\\%was MemoryOS’s abstain rate\.Appendix[Z](https://arxiv.org/html/2609.10413#A26)corpus size5,344/3,892/133\.6→18,936/12,968/324\.25\{,\}344/3\{,\}892/133\.6\\to 18\{,\}936/12\{,\}968/324\.2Stale proof\-of\-concept snapshot\.λother\\lambda\_\{\\textsc\{other\}\}0\.0030→0\.00500\.0030\\to 0\.0050in Table[49](https://arxiv.org/html/2609.10413#A22.T49)Two tables disagreed;0\.00500\.0050is the deployed and released value\. Zero result changes\.Perturbation flip countsdenominator now stated≈910\\approx 910/≈4,400\\approx 4\{,\}400are10%10\\%/50%50\\%of8,9138\{,\}913affected edge\-instances, not of the6,1806\{,\}180unique eligible entries\.Polytope cell count“45 off\-diagonal”→\\to45 populated \(5 diagonal, 40 off\-diagonal\)The artifact records 45 cells in total\.αFmax=0\.065\\alpha\_\{F\}^\{\\max\}=0\.065,αLmin=0\.138\\alpha\_\{L\}^\{\\min\}=0\.138now attributed to FR\-GraphitiFR\-Bank’s artifact values are1\.7×10−61\.7\\times 10^\{\-6\}and≈1\.0\\approx 1\.0; the medians are from the FR\-Graphiti\-era analysis\.One further disclosure\. During the discussion period we quoted a figure of12\.5%12\.5\\%for AV8 numeric preservation under a uniform blending weight\. That figure appears only in prose in earlier drafts and is reproduced by no released artifact; the two artifacts that come closest to testing it report81\.0%81\.0\\%\(the uniform ontology\-ablation arm over 516 questions\) and a degenerate Phase\-2\-era value\. We therefore withdraw it and make the calibration argument in §[4](https://arxiv.org/html/2609.10413#S4)entirely from artifact\-backed quantities:99\.8%99\.8\\%of1,5661\{,\}566cross\-pairs infeasible, zero feasible cells among the 45 populated, andmin⁡αFmax=1\.7×10−6\\min\\alpha\_\{F\}^\{\\max\}=1\.7\\times 10^\{\-6\}againstmax⁡αLmin≈1\.0\\max\\alpha\_\{L\}^\{\\min\}\\approx 1\.0\.

A targeted audit of suspected items produced the corrections above; a stratified random audit of roughly 60 additional measured cells—the 45 per\-AV cells of Table[26](https://arxiv.org/html/2609.10413#A4.T26), the 11 decay\-rate cells, the LongMemEval variance bounds, and the latency table—found no mismatches\. The errors are confined to the editing layer: stale runs transcribed into tables, sign and label slips, and aggregate typos\. The measurement layer, meaning the per\-question records, banks and configurations, is unaffected, and all raw records are released\.

## NeurIPS Paper Checklist

1. 1\.Claims
2. Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
3. Answer:\[Yes\]
4. Justification: All main claims are supported by experiments described in §[6](https://arxiv.org/html/2609.10413#S6)and theoretical analysis in §[4](https://arxiv.org/html/2609.10413#S4)with proofs in Appendix[A](https://arxiv.org/html/2609.10413#A1)\.
5. 2\.Limitations
6. Question: Does the paper discuss the limitations of the work performed by the authors?
7. Answer:\[Yes\]
8. Justification: Limitations are discussed in §[7](https://arxiv.org/html/2609.10413#S7)\(rate\-calibration generalization, soft\-supersession failure mode under high\-commitment generators, classifier validation via LLM judges, and the scope of the ontology’s value across distant vs\. nearby category distinctions\)\.
9. 3\.Theory assumptions and proofs
10. Question: For each theoretical result, does the paper provide the full set of assumptions and a complete \(and correct\) proof?
11. Answer:\[Yes\]
12. Justification: All theoretical results \(Theorems 1–4, the lifecycle non\-identifiability and individual\-necessity results, and the staleness\-decomposition propositions\) include formal statements and complete proofs in Appendix[A](https://arxiv.org/html/2609.10413#A1)\.
13. 4\.Experimental result reproducibility
14. Question: Does the paper fully disclose all the information needed to reproduce the main experimental results?
15. Answer:\[Yes\]
16. Justification: Benchmark data \(40 personas, 1,400 sessions, 516 questions, ground truth\) and FR\-Bank code are released as supplementary material and will be made publicly available upon publication\. All model versions, hyperparameters, and evaluation protocols are documented in Appendix[C](https://arxiv.org/html/2609.10413#A3), Appendix[U](https://arxiv.org/html/2609.10413#A21), and Appendix[V](https://arxiv.org/html/2609.10413#A22)\.
17. 5\.Open access to data and code
18. Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results?
19. Answer:\[Yes\]
20. Justification: LifecycleBench \(questions, personas, ground truth\), FR\-Bank source code, all evaluation results, and run logs are publicly archived at[https://doi\.org/10\.5281/zenodo\.20067778](https://doi.org/10.5281/zenodo.20067778)\(DOI:10\.5281/zenodo\.20067778\) and bundled with the supplementary material\. Run scripts and exact configurations are included\.
21. 6\.Experimental setting/details
22. Question: Does the paper specify all the training and test details \(e\.g\., data splits, hyperparameters, optimizer, type of compute\) necessary to understand the results?
23. Answer:\[Yes\]
24. Justification: Evaluation methodology, model versions, and hyperparameters are fully described in Appendices[C](https://arxiv.org/html/2609.10413#A3),[O](https://arxiv.org/html/2609.10413#A15),[P](https://arxiv.org/html/2609.10413#A16),[N](https://arxiv.org/html/2609.10413#A14), and[AB](https://arxiv.org/html/2609.10413#A28)\.
25. 7\.Experiment statistical significance
26. Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
27. Answer:\[Yes\]
28. Justification: Bootstrap confidence intervals and pairwise significance tests are reported in Appendix[D\.6](https://arxiv.org/html/2609.10413#A4.SS6); LongMemEval\-S run\-to\-run variance is reported in Table[15](https://arxiv.org/html/2609.10413#A4.T15); the 20/20 persona holdout split \(Fisher’sp=1\.00p=1\.00\) is reported in §[7](https://arxiv.org/html/2609.10413#S7)\.
29. 8\.Experiments compute resources
30. Question: For each experiment, does the paper provide sufficient information on the computer resources \(type of compute workers, memory, time of execution\) needed to reproduce the experiments?
31. Answer:\[Yes\]
32. Justification: All evaluations are API\-driven and require no GPU training\. The deterministic lifecycle layer’s latency \(median47​μ​s47\\,\\mu\\mathrm\{s\}, single\-threaded Python on AMD Zen 3\) is reported in §[3](https://arxiv.org/html/2609.10413#S3)and Appendix[B](https://arxiv.org/html/2609.10413#A2); per\-system API call counts and Kimi K2\.5 cross\-generator API cost \(under $10\) are documented in Appendix[AB](https://arxiv.org/html/2609.10413#A28)\.
33. 9\.Code of ethics
34. Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics?
35. Answer:\[Yes\]
36. Justification: All evaluations use synthetic personas \(no human subjects\), publicly available APIs, and openly licensed competitor code \(Mem0 Apache 2\.0, A\-MEM/Memory\-R1/MemoryOS as published\)\. No private or personally identifiable data is used\.
37. 10\.Broader impacts
38. Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
39. Answer:\[Yes\]
40. Justification: Memory systems that retain personal information raise privacy concerns; the interpretability and selective\-forgetting capabilities of FR provide users with control over their data\. Privacy, consent, and safety considerations are discussed in §[7](https://arxiv.org/html/2609.10413#S7)and Appendix[AC\.1](https://arxiv.org/html/2609.10413#A29.SS1)\.
41. 11\.Safeguards
42. Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse?
43. Answer:\[Yes\]
44. Justification: The released benchmark contains only synthetic personas\. Prompt\-injection detection and confidence\-degradation mechanisms in the ingestion classifier are described in Appendix[B](https://arxiv.org/html/2609.10413#A2); production deployment recommendations regarding consent and verifiable deletion are in Appendix[AC\.1](https://arxiv.org/html/2609.10413#A29.SS1)\.
45. 12\.Licenses for existing assets
46. Question: Are the creators or original owners of assets \(e\.g\., code, data, models\), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
47. Answer:\[Yes\]
48. Justification: Mem0 \(Apache 2\.0\), A\-MEM, Memory\-R1, MemoryOS, and Zep/Graphiti are cited and credited; Kimi K2\.5 is released under a Modified MIT License; OpenAI and Anthropic models are accessed via publicly available APIs\. Embedding models \(text\-embedding\-3\-small\) are similarly cited\.
49. 13\.New assets
50. Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
51. Answer:\[Yes\]
52. Justification: LifecycleBench \(516 questions, 40 personas, structured YAML ground truth, 9 attack vectors\) and FR\-Bank source code are released as supplementary material with documentation, and will be made publicly available under an open license upon publication\.
53. 14\.Crowdsourcing and research with human subjects
54. Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation \(if any\)?
55. Answer:\[N/A\]
56. Justification: No crowdsourcing or research with human subjects was performed\. All personas are synthetic; all classifier\-agreement audits use LLM judges, not human annotators\.
57. 15\.Institutional review board \(IRB\) approvals or equivalent for research with human subjects
58. Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board \(IRB\) approvals \(or an equivalent approval/review based on the requirements of your country or institution\) were obtained?
59. Answer:\[N/A\]
60. Justification: No human subjects were involved\.
61. 16\.Declaration of LLM usage
62. Question: Does the paper describe the usage of LLMs if it is an important, original, or non\-standard component of the core method development in this research?
63. Answer:\[Yes\]
64. Justification: The Fortunate Recall pipeline uses LLMs at ingestion \(onegpt\-4\.1\-minicall per turn for entity/edge extraction and behavioral classification\) and a single lightweight LLM call at retrieval \(gpt\-4\.1\-mini distillation\)\. The LLM/lifecycle\-math boundary is documented explicitly in §[3](https://arxiv.org/html/2609.10413#S3)and Figure[1](https://arxiv.org/html/2609.10413#S3.F1), and downstream answer generation uses GPT\-5\.4 \(primary\) and Kimi K2\.5 \(cross\-generator validation\)\.