Parametric Session States Recover Retrieval Intent without Replaying History

# Parametric Session States Recover Retrieval Intent without Replaying History
Source: [https://arxiv.org/html/2610.33047](https://arxiv.org/html/2610.33047)
Dianyun WangAffiliation:Beijing University of Posts and TelecommunicationsEmail:[dianyunwang@bupt\.edu\.cn](mailto:)Jiahong LiuAffiliation:The Chinese University of Hong KongEmail:[jiahong\.liu21@gmail\.com](mailto:)Irwin KingAffiliation:The Chinese University of Hong KongEmail:[king@cse\.cuhk\.edu\.hk](mailto:)

###### Abstract

Long\-running assistants often interpret follow\-up requests whose referents, constraints, and active goals were established many turns earlier\. The central challenge is therefore not only context length, but retrieval intent: a current query such as “use the previous configuration” may omit the project, entity, and version terms needed to locate relevant evidence\. Long\-context models can recover those terms by replaying the interaction, but repeatedly pay the cost of processing history\. Conventional retrieval\-augmented generation \(RAG\) is cheaper, yet assumes an information\-sufficient query; conversational rewriting either rereads the history or depends on an explicitly maintained textual memory\. We introduce*Parametric Session State*\(PSS\), a reusable session\-memory layer that remembers what to search for while keeping factual knowledge external\. An offline writer compiles the ordered interaction together with retrieval supervision into a fixed\-shape, session\-specific LoRA state\. At query time, the state briefly produces a compact, retrieval clue; the system then retrieves inspectable source text, unloads the state, and lets the frozen base model answer from that evidence\. Across controlled and sessionized public evaluations, correct PSS states improve target\-evidence retrieval for underspecified follow\-ups\. On the registered controlled and public tracks, matched\-wrong and shuffled controls attribute the gains to the corresponding session, and the retrieval benefit transfers across model families and heterogeneous backends\. A three\-seed carrier confirmation isolates ordered\-history information beyond supplied retrieval targets and measures a 6\.25\-point gain over a 256\-token text memory on BGE\-M3\. These results establishPSSas an effective retrieval\-supervised memory carrier for RAG: it restores missing session scope, supports strong evidence access across diverse systems, and preserves an external, auditable knowledge store\.

## 1Introduction

Long\-running assistants accumulate more context than a user will restate in every request\. Consider a research agent that has discussed several projects, checkpoints, and superseded configurations\. The follow\-up “rerun the previous configuration” is meaningful inside the session, but nearly useless as a standalone search query: the terms that identify the active project and version are absent\. In this setting, RAG can fail*before retrieval begins*: as[Figure1](https://arxiv.org/html/2610.33047#S1.F1)illustrates, the identifiers that resolve “previous” remain in history while the retriever sees only the raw query\. A stronger encoder alone does not recover information absent from the query\. We study the following problem:*can a long session leave a reusable state that restores its retrieval intent without replaying historical tokens at every query?*

Existing systems expose a difficult trade\-off\. Long\-context models and KV compression replay or retain token\-dependent activations, preserving access to the history but paying a cost that grows with it\([Xiao et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib31);[Nawrot et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib25);[Li et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib20)\)\. Textual memories, summaries, and conversational query rewriting reduce that cost by making the relevant state explicit, and they usually read history again when producing the rewrite\([Wu et al\., 2022](https://arxiv.org/html/2610.33047#bib.bib30)\)\. Standard RAG stores precise facts externally and is easy to audit, yet assumes an information\-sufficient query\([Lewis et al\., 2020](https://arxiv.org/html/2610.33047#bib.bib19)\)\. Global\-memory RAG and parametric document modules encode long inputs more deeply\([Qian et al\., 2025](https://arxiv.org/html/2610.33047#bib.bib26);[Caccia et al\., 2025](https://arxiv.org/html/2610.33047#bib.bib3);[Eyuboglu et al\., 2026](https://arxiv.org/html/2610.33047#bib.bib8)\), but primarily target document understanding or direct answering rather than a session whose present query is underspecified\.

Figure 1:Failure mode of conventional RAG under an underspecified follow\-up\. Session identifiers are absent from the raw query, placing the intended evidence outside the returned top\-kk\.This leaves two linked gaps\. The*systems gap*is the absence of a reusable layer between session history and retrieval: RAG needs a representation of*what this session is currently about*that can restore missing query scope while leaving exact facts in the external store\. The*evaluation gap*is the absence of a test that isolates this capability\. Ordinary long\-context benchmarks usually present self\-contained questions, so success can come from the current query alone rather than recovered conversational scope\. A memory/no\-memory comparison remains ambiguous because a generic adapter may improve query style without encoding the corresponding session\. Identifying session\-memory effects therefore requires underspecified queries, session\-disjoint splits, matched\-wrong and shuffled states, null/OOD probes, and session\-level paired statistics\.

To bridge the two gaps, we pair a retrieval architecture with an identification protocol\. For the systems gap, we propose*Parametric Session State*\(PSS\): an offline writer compiles ordered historyHsH\_\{s\}together with positive and negative retrieval targets into a fixed\-rank LoRA stateΔs\\Delta\_\{s\}\. The state conditions a short online clue that restores missing project, entity, relation, or version terms\. The clue retrieves evidence from the external corpus; the state is then unloaded and the frozen base model answers from the retrieved text\. An optional guard can select raw, text\-card, or state\-assisted retrieval from observable utility signals\. For the evaluation gap, we make the current query deliberately underspecified, exclude formal answers from the writer, freeze the corpus and retrieval stack, and contrast corresponding states with wrong, shuffled, zero, null, and OOD conditions at the session level\. This paired design makes the claim falsifiable: in the*write–retrieve–unload*architecture, parameters should recover session scope while precise facts remain external and auditable\.

We evaluate whether this mechanism generalizes across public data, model families, and retrieval backends\. We derive session protocols from LongBench/InfiniteBench QA tasks\([Bai et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib2);[Zhang et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib33)\)and UltraDomain, and freeze the same state design across multiple language\-model families\([Hui et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib14);[Jiang et al\., 2023](https://arxiv.org/html/2610.33047#bib.bib16);[Abdin et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib1)\)\. Correct, matched\-wrong, shuffled, and zero states test whether retrieval changes for the corresponding session; heterogeneous retrievers test whether the clue transfers beyond its writer; and same\-evidence answer ablations test the value of keeping the state loaded after retrieval\. We then introduce PSS\-320, a controlled collection of technical sessions with ambiguous, compositional, temporal, null, and conflict probes, to isolate causal effects and robustness properties that ordinary self\-contained QA rarely exposes\.

Our contributions and findings are:

- •A retrieval\-scoped parametric session memory\.We introducePSS, a framework that uses a bounded, session\-specific LoRA state as a carrier for retrieval intent\. Its write–retrieve–unload lifecycle reconstructs what to search for while leaving precise claims in external, inspectable evidence\.
- •An evaluation designed for missing retrieval intent\.We introduce public sessionization and PSS\-320, combining a shared candidate corpus, disjoint splits, causal state controls, null/OOD probes, and session\-level inference to distinguish recovered session scope from generic query improvement\.[SectionB\.2](https://arxiv.org/html/2610.33047#A2.SS2)gives the full motivation and design\.
- •Generalization and mechanism evidence\.Correct states substantially improve retrieval over ambiguous queries and causal controls across three model families and heterogeneous lexical, dense, hierarchical, graph\-compatible, and query\-transformation backends\. A three\-seed confirmation shows that ordered history contributes retrieval signal beyond supplied targets, while state\-fingerprint and functional\-alignment analyses connect the learned carrier to session\-specific outputs\.

## 2Method

![Refer to caption](https://arxiv.org/html/2610.33047v1/figures/newmethod.png)

Figure 2:Parametric Session State workflow\.An offline writer compiles the ordered history and positive/negative clue supervision into a session\-specific adapter through consecutive LM and readout phases\. At inference, the adapter generates a retrieval clue and is unloaded before the frozen base model answers from retrieved evidence\.### 2\.1Problem formulation

#### Inputs and frozen components\.

For sessionss, letHs=\(h1,…,hT\)H\_\{s\}=\(h\_\{1\},\\ldots,h\_\{T\}\)be the ordered interaction history,qsq\_\{s\}the current underspecified query, and𝒟\\mathcal\{D\}a shared external corpus of source chunks\. The deployed RAG system contains a frozen retrieverRϕR\_\{\\phi\}and a frozen answer modelpθp\_\{\\theta\}\. During evaluation only, letEs⋆⊂𝒟E\_\{s\}^\{\\star\}\\subset\\mathcal\{D\}denote the target evidence; neitherEs⋆E\_\{s\}^\{\\star\}nor the formal answer is an input to the writer or online system\. A full\-context reader can resolve references throughpθ​\(y∣Hs,qs\)p\_\{\\theta\}\(y\\mid H\_\{s\},q\_\{s\}\), whereas standard RAG retrievesRϕ​\(qs,𝒟\)R\_\{\\phi\}\(q\_\{s\},\\mathcal\{D\}\)and fails when the identifying terms occur only inHsH\_\{s\}\.

#### Framework contract\.

PSS is a retrieval\-scoped parametric memory framework: it changes the query\-interpretation layer while leaving the external index, retriever, and answer model unchanged\. Let𝒮s=\(zs\+,zs−\)\\mathcal\{S\}\_\{s\}=\(z\_\{s\}^\{\+\},z\_\{s\}^\{\-\}\)denote the offline, writer supervision used in our implementation: a positive search clue and a same\-type archived or conflicting clue\. An optimization\-based compiler𝒜λ\\mathcal\{A\}\_\{\\lambda\}writes an architecture\-compatible, bounded state, which is invoked only to reconstruct a search clue:

Δs\\displaystyle\\Delta\_\{s\}=𝒜λ​\(Hs,𝒮s,θ,𝒞θ\),\\displaystyle=\\mathcal\{A\}\_\{\\lambda\}\(H\_\{s\},\\mathcal\{S\}\_\{s\};\\theta,\\mathcal\{C\}\_\{\\theta\}\),q~s\\displaystyle\\tilde\{q\}\_\{s\}=Gθ\+Δs​\(qs\),\\displaystyle=G\_\{\\theta\+\\Delta\_\{s\}\}\(q\_\{s\}\),\(1\)Es\\displaystyle E\_\{s\}=TopKk⁡Rϕ​\(q~s,𝒟\),\\displaystyle=\\operatorname\{TopK\}\_\{k\}R\_\{\\phi\}\(\\tilde\{q\}\_\{s\},\\mathcal\{D\}\),ys\\displaystyle y\_\{s\}∼pθ​\(y∣qs,Es\)\.\\displaystyle\\sim p\_\{\\theta\}\(y\\mid q\_\{s\},E\_\{s\}\)\.The history and writer supervision are offline\-only\. At inference,Δs\\Delta\_\{s\}is loaded briefly, emits the clueq~s\\tilde\{q\}\_\{s\}, and is unloaded before the frozen base model answers from retrieved evidenceEsE\_\{s\}\. Formal answers and target\-document identifiers are excluded from𝒮s\\mathcal\{S\}\_\{s\}\.

#### Desired improvement\.

LetU⁡\(E,E⋆\)U\(E,E^\{\\star\}\)be an evidence utility such as target\-document recall\. The desired state improves evidence access for an ambiguous follow\-up while remaining bounded and eliminating online history replay:

Δs⋆∈arg⁡maxΔ∈𝒞θ\\displaystyle\\Delta\_\{s\}^\{\\star\}\\in\\arg\\max\_\{\\Delta\\in\\mathcal\{C\}\_\{\\theta\}\}U⁡\(TopKk⁡Rϕ​\(Gθ\+Δ​\(qs\),𝒟\),Es⋆\)\\displaystyle U\\\!\\left\(\\operatorname\{TopK\}\_\{k\}R\_\{\\phi\}\\bigl\(G\_\{\\theta\+\\Delta\}\(q\_\{s\}\),\\mathcal\{D\}\\bigr\),E\_\{s\}^\{\\star\}\\right\)\(2\)s\.t\.\\displaystyle\\text\{s\.t\. \}bytes\(Δ\)≤B,Hs∉online inputs,θ,ϕfrozen\.\\displaystyle\\operatorname\{bytes\}\(\\Delta\)\\leq B,\\quad H\_\{s\}\\notin\\text\{online inputs\},\\quad\\theta,\\phi\\text\{ frozen\}\.The gold setEs⋆E\_\{s\}^\{\\star\}and its identifiers appear only in this evaluation objective, not in the compiler or deployed system; the compiler instead uses the clue supervision defined above\. Because our implementation does not differentiate through retrieval,[Equation4](https://arxiv.org/html/2610.33047#S2.E4)provides a retrieval\-aligned surrogate\. The intended gain is evidence access under missing intent\.[AppendixA](https://arxiv.org/html/2610.33047#A1)gives the complete offline and online contracts\.

### 2\.2LoRA as a bounded session\-state carrier

LoRA supplies the bounded state carrier in our implementation; the PSS contribution is the session\-specific state contract and retrieval lifecycle built around it\. For a frozen autoregressive modelθ\\theta, let𝒞θ\\mathcal\{C\}\_\{\\theta\}specify a set of writable layer–projection pairs\. The compiler creates one low\-rank update for each pair,

Wℓ,m\(s\)=Wℓ,m\+αr​Bℓ,m\(s\)​Aℓ,m\(s\),\(ℓ,m\)∈𝒞θ,W^\{\(s\)\}\_\{\\ell,m\}=W\_\{\\ell,m\}\+\\frac\{\\alpha\}\{r\}B^\{\(s\)\}\_\{\\ell,m\}A^\{\(s\)\}\_\{\\ell,m\},\\qquad\(\\ell,m\)\\in\\mathcal\{C\}\_\{\\theta\},\(3\)while the base parameters remain frozen\. The compiler optimizes only these session\-local factors and serializes them asΔs\\Delta\_\{s\}\. Projection names, fused modules, and writable layers may vary by backbone; the functional contract remains fixed: one session produces one bounded state, the state produces a textual retrieval interface, and it is removed before answering\. Unlike conventional task LoRA, the adapter is not a shared task solution and does not remain active for final generation\.

Qwen2\.5\-7B is the primary concrete instance\([Hui et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib14)\); Mistral\-7B and Phi\-3\-mini instantiate the same contract with their native projection layouts\. Each model writes its own rank\-32, single\-slot BF16 state, with no tensor transfer across backbones\. Layer placement, optimization steps, and state\-size accounting are reported in[AppendicesJ](https://arxiv.org/html/2610.33047#A10)and[R](https://arxiv.org/html/2610.33047#A18)\.

### 2\.3Retrieval\-aligned session compilation

The selectedretrieval\_alignedcompiler first optimizes history language modeling over bounded chunks, then optimizes clue readout while retaining the same state\. Each phase initializes its own optimizer at the registered learning rate\. Letzs\+z\_\{s\}^\{\+\}be a clue assembled from write\-time session scope and evidence\-related fields represented in the history, and letzs−z\_\{s\}^\{\-\}be a same\-type archived or conflicting clue\.The readout term is

ℒret=ℓ⁡\(zs\+\)\+max⁡\(0,m\+ℓ⁡\(zs\+\)−ℓ⁡\(zs−\)\),\\mathcal\{L\}\_\{\\mathrm\{ret\}\}=\\ell\(z\_\{s\}^\{\+\}\)\+\\max\\left\(0,\\,m\+\\ell\(z\_\{s\}^\{\+\}\)\-\\ell\(z\_\{s\}^\{\-\}\)\\right\),\(4\)whereℓ\\ellis teacher\-forced sequence negative log likelihood andm=0\.2m=0\.2\. The primary readout phase uses a fixed session\-clue instruction\. Its supervision is constructed automatically: PSS\-320 uses controlled session fields also represented in the history, while the public protocol uses history\-parsed active requests as positive targets and same\-task requests from other sessions as negatives\. In these protocols, target construction requires no per\-session manual clue annotation and does not read future follow\-up probes, formal answers, or target\-document IDs\. A deployment can supply these write\-time inputs through existing session metadata or a history\-to\-target extractor\. Our controlled evaluation examines how history and the resulting supervision are compiled into reusable parameters and accessed for retrieval, with the upstream session associations explicitly available\. A separate question\-conditioned extension with multiple historical records is evaluated in[SectionV\.3](https://arxiv.org/html/2610.33047#A22.SS3)\. Objective, content, rank, topology, and precision ablations are detailed in[AppendicesJ](https://arxiv.org/html/2610.33047#A10)and[D](https://arxiv.org/html/2610.33047#A4)\.

### 2\.4Intent readout, retrieval, and unloading

The core path,*PSS clue retrieval*, loadsΔs\\Delta\_\{s\}, generatesq~s\\tilde\{q\}\_\{s\}, and exposes that text to a retriever\. This textual boundary makes the memory layer compatible with lexical, dense, hierarchical, graph, and query\-transformation backends\. The*Raw \+ PSS RRF*ablation unconditionally fuses raw\-query and PSS\-clue rankings according to

RRF⁡\(d\)=∑r∈\{raw,PSS\}160\+rankr​\(d\)\\mathrm\{RRF\}\(d\)=\\sum\_\{r\\in\\\{\\mathrm\{raw\},\\mathrm\{PSS\}\\\}\}\\frac\{1\}\{60\+\\mathrm\{rank\}\_\{r\}\(d\)\}\(5\)\([Cormack et al\., 2009](https://arxiv.org/html/2610.33047#bib.bib7)\)\.Guarded PSSadditionally routes among raw, structured card, and PSS\-RRF using only observable retrieval features; its cross\-fitting and safety contract appear in[AppendixK](https://arxiv.org/html/2610.33047#A11)\. The complete guarded path includes the card’s text input and both clue generators; its measured call and token counts are reported in[SectionV\.5](https://arxiv.org/html/2610.33047#A22.SS5)\.

After retrieval, the adapter is unloaded and the frozen base model answers from\(qs,Es\)\(q\_\{s\},E\_\{s\}\)\. A same\-query, same\-evidence ablation varies only the answer\-stage state, isolating decoder effects from retrieval effects \([AppendixP](https://arxiv.org/html/2610.33047#A16)\)\. The state is fixed\-size per session, although offline write compute grows with history and total storage grows with the number of sessions; complete accounting is deferred to[AppendixR](https://arxiv.org/html/2610.33047#A18)\.

## 3Experiments

We organize the main evaluation around three questions\.RQ1: Does PSS recover retrieval intent across data, models, and retrievers?RQ2: Do functional outputs align with session\-specific intent?RQ3: Which design choices produce the gain?We report the online serving cost alongside retrieval utility; full storage and amortization profiles appear in[AppendicesR](https://arxiv.org/html/2610.33047#A18)and[V\.5](https://arxiv.org/html/2610.33047#A22.SS5)\.

### 3\.1Evaluation design

We hold the corpus, index, retriever, and reader fixed within each primary protocol and vary the query source or session state\. Public sessionizations test transfer; PSS\-320 uses a shared cross\-session corpus and state interventions to identify session memory\.*PSS clue retrieval*searches with the generated clue,*PSS\-RRF*fuses raw and clue rankings, and*Guarded PSS*routes among raw, card, and PSS\-RRF\. Fixed\-question QA then tests whether better evidence improves answering after state unloading\. Evaluation rationale and full method definitions appear in[SectionsB\.1](https://arxiv.org/html/2610.33047#A2.SS1)and[B\.2](https://arxiv.org/html/2610.33047#A2.SS2)\.

### 3\.2Experimental setup

We evaluate one frozen PSS recipe in three complementary settings: a sealed 262\-session transformation of seven LongBench/InfiniteBench QA tasks, a 112\-session UltraDomain transfer set, and PSS\-320, whose shared candidate corpus supports a source\-group\-disjoint 256\-session test\. Public tracks report target\-document All\-Recall@3; PSS\-320 reports all\-support evidence recall atk=4k=4\. Correct, matched\-wrong, shuffled, zero, null, and OOD conditions isolate session\-specific memory from generic adapter or rewrite effects\.

Qwen2\.5\-7B is the primary backbone; Mistral\-7B and Phi\-3\-mini test portability, and lexical, dense, hierarchical, graph, and query\-transformation retrievers test the textual clue interface\. Primary state\-writing evaluations use writer seeds 91–93; follow\-up protocols specify their seed counts separately\. Sessions are the unit of inference\. We use paired bootstrap intervals, registered McNemar/sign\-flip tests, and Holm correction\([Tibshirani & Efron, 1993](https://arxiv.org/html/2610.33047#bib.bib28);[Holm, 1979](https://arxiv.org/html/2610.33047#bib.bib12)\); daggers are emitted only when every registered comparison passes\. Dataset construction, frozen registrations, model contracts, baselines, prompts, and statistical gates are given in[AppendicesB](https://arxiv.org/html/2610.33047#A2),[I](https://arxiv.org/html/2610.33047#A9),[J](https://arxiv.org/html/2610.33047#A10),[M](https://arxiv.org/html/2610.33047#A13),[L](https://arxiv.org/html/2610.33047#A12)and[S](https://arxiv.org/html/2610.33047#A19)\.

### 3\.3RQ1: Retrieval\-intent recovery generalizes

Figure 3:Session\-weighted target\-document retrieval and isolated\-reader answer F1 on 262 sealed public sessions \(percent\)\. F1 evaluates the complete query\-and\-evidence interface; fixed\-question evidence attribution is reported separately in[Table1](https://arxiv.org/html/2610.33047#S3.T1)\.#### LongBench and InfiniteBench\.

On the 262 sealed public sessions, Qwen PSS clue retrieval with the correct session state improves All\-Recall@3 over raw, wrong\-state, and shuffled\-state queries by 35\.88, 31\.30, and 48\.09 points, respectively \(allpHolm=5\.99994×10−5p\_\{\\mathrm\{Holm\}\}=5\.99994\\times 10^\{\-5\}\)\. On the five multi\-document tasks, PSS reaches 77\.50–100% versus 30\.00–57\.50% for raw retrieval; PSS\-RRF reaches 82\.50% on Qasper\. En\.QA and NarrativeQA saturate because each constructed session indexes one shared document \([Table10](https://arxiv.org/html/2610.33047#A7.T10)\)\. The parsed active\-request reference directly retrieves with the complete request designated by the protocol’s activity marker, measuring text retrieval with request selection already resolved\. PSS uses this same request as positive readout supervision and compiles it together with history into a reusable parameter state\. The multi\-record extension tests question\-conditioned access to one compiled state \([SectionV\.3](https://arxiv.org/html/2610.33047#A22.SS3)\)\. Under the original query\-and\-evidence interface, answer F1 changes from 1\.03% to 20\.00%\. Router\-transfer and null/OOD results appear in[AppendixF](https://arxiv.org/html/2610.33047#A6)\.

#### Retrieved evidence improves answering\.

A registered follow\-up fixes each reader’s source question on the same 262\-session split and varies the retrieved top\-3 chunks, with PSS unloaded\. Controlled F1 improves over raw\-query evidence by 10\.60, 4\.06, and 4\.83 points for Qwen, Mistral, and Phi\-3, respectively \(allpH=0\.0003p\_\{H\}=0\.0003;[Table1](https://arxiv.org/html/2610.33047#S3.T1)\)\. For Qwen, PSS also improves over the cross\-domain ConvSearch\-R1 checkpoint by 3\.48 points \(95% CI\[1\.51,5\.57\]\[1\.51,5\.57\],pH=0\.006p\_\{H\}=0\.006\)\. Retrieval interfaces remain unchanged\. Complete contrasts, the UltraDomain replication, and an independent 16\-session evidence control appear in[SectionsG\.2](https://arxiv.org/html/2610.33047#A7.SS2)and[V\.4](https://arxiv.org/html/2610.33047#A22.SS4)\.

Table 1:Controlled answer F1 \(percent\) in the 262\-session public follow\-up\. Each reader receives a method\-invariant source question and method\-retrieved top\-3 evidence, with history hidden and PSS unloaded\. All four query sources are retained; complete retrieval and paired results appear in[SectionG\.2](https://arxiv.org/html/2610.33047#A7.SS2)\.Query sourceQwen2\.5\-7BMistral\-7BPhi\-3\-miniAmbiguous raw query4\.626\.548\.61Parsed ref\.14\.9611\.3216\.03ConvSearch\-R111\.7410\.0211\.81PSS clue retrieval15\.2210\.6013\.44
#### UltraDomain\.

On the UltraDomain transformation, correct states reach 98\.21–99\.11% All\-Recall@3 across all three backbones, improving the already strong raw\-query recall by 1\.79–4\.46 points\. The gains are positive for every backbone\. This result extends the method to financial, legal, and mixed\-domain documents\.

#### Controlled PSS\-320 mechanism test\.

The raw underspecified query retrieves all required evidence with probability 0\.1734\. A compact 32\-token structured card and 128\-token summary reach 0\.3945 and 0\.4023\. PSS clue retrieval reaches 0\.5008 with no online historical text, improving over the compact card by 10\.63 points\. The completeGuarded PSSsystem reaches 0\.5063, an 11\.18\-point gain over that card, while retaining its card\-based routing branch\. These results establish the value of parameterized session scope against compact text\-state baselines\.[AppendixV](https://arxiv.org/html/2610.33047#A22)separates these cards from parsed request references and supplied\-clue caches, and reports complete readout controls\.

The paired effects pass H1/H2\.Guarded PSScorrects 134 sessions missed by raw retrieval, with no raw\-only success; against the card, there are 56 Guarded\-PSS\-only and seven card\-only successes\. WithinGuarded PSS, the reported correct\-state performance exceeds the matched\-wrong and parameter\-shuffled controls by 0\.1750 and 0\.1211 in All\-Recall@4, respectively\. These contrasts support session\-specific state contributions within the guarded retrieval system\.

Figure 4:Retrieval utility and online workload\.\(a\) Original 256\-session PSS\-320 test aggregation\. \(b\) Separate eight\-session profile andK=16K=16memory experiment\. Columns count generations, evidence queries, and mean memory tokens supplied to LLMs; zero memory input does not imply an absent text cache\. Each block retains its generation budget\. Workload components exclude final answering and offline writing; measured timings and full accounting appear in[SectionsV\.3](https://arxiv.org/html/2610.33047#A22.SS3)and[V\.5](https://arxiv.org/html/2610.33047#A22.SS5)\.
#### Online retrieval workload\.

[Figure4](https://arxiv.org/html/2610.33047#S3.F4)\(b\) separates generation calls, evidence queries, and memory\-text input\. PSS uses one generation and one evidence query, with no memory\-text input to the LLM\. AtK=16K=16, it replaces record\-wise fusion’s 16 queries with one and reaches 83\.75/95\.00% All\-Recall@4 \(BGE\-M3/BM25\)\. Grok\-based record selection accesses the persistent text bank through an external model API before evidence retrieval\. PSS performs question\-conditioned readout from its compiled parameter state without supplying the text bank to the readout model \([SectionV\.3](https://arxiv.org/html/2610.33047#A22.SS3)\)\.

#### Cross\-model and cross\-retriever summary\.

Across all three backbones, PSS improves public\-session retrieval by 33\.97–35\.88 points and passes the matched\-wrong and shuffled controls\. On PSS\-320, state clues improve BGE\-M3 by 21\.48–45\.63 points and the graph\-compatible retriever by 32\.11–53\.13 points; every state row also exceeds its card baseline and receives a script\-computed dagger\. Independently written states therefore preserve the same retrieval\-intent function across three model architectures\.

Table 2:Transfer across backbones and retrieval backends \(percent\)\. Panel A reports the formal cross\-model evaluation: Public and Ultra use target\-document All\-Recall@3; BGE\-M3 and GraphRAG use PSS\-320 evidence All\-Recall@4\. Panel B is a disjoint 112\-session public strong\-backend confirmation\. Sup\. denotes positive Holm\-corrected effects over raw, wrong, and shuffled states for the same frozen backend\. Panel A’s PSS\-320 card comparisons use compact structured cards; Panel B uses the parsed active\-request reference \(“Parsed ref\.”\)\.†\\daggerin Panel A marks PSS\-320 states that beat raw and card\. Asterisks identify compatible HyDE/RQ\-RAG pipelines\. Arrows indicate the preferred direction: higher recall and gains, and lower state storage\.Panel A: cross\-model evaluation\. PublicBGE\-M3GraphRAGUltraModelRaw↑\\uparrowPSS↑\\uparrowSup\.Raw↑\\uparrowPSS↑\\uparrowRaw↑\\uparrowPSS↑\\uparrowRaw↑\\uparrowPSS↑\\uparrowSup\.State MiB↓\\downarrowQwen2\.5\-7B60\.6996\.56yes12\.4233\.91†16\.3348\.44†96\.4398\.21no44Mistral\-7B61\.8395\.80yes12\.0351\.09†16\.3367\.66†94\.6498\.21no40Phi\-3\-mini60\.6995\.80yes11\.9557\.58†16\.0969\.22†94\.6499\.11no24

Panel B: frozen\-backend public confirmation \(n=112n=112sessions; disjoint from the smoke set\)\. RetrieverRaw↑\\uparrowFull hist\.↑\\uparrowParsed ref\.↑\\uparrowPSS clue↑\\uparrowΔ\\Deltavs\. raw↑\\uparrowWrong↑\\uparrowShuffled↑\\uparrowPSS\-RRF↑\\uparrowGold↑\\uparrowSup\.BM2566\.0769\.6483\.9384\.82\+18\.7571\.4359\.8284\.8283\.93noContriever69\.6478\.5798\.21100\.00\+30\.3667\.8652\.6899\.1198\.21yesBGE\-M363\.3977\.6898\.2199\.11\+35\.7164\.2951\.7997\.3298\.21yesQwen3\-Embedding\-4B69\.6480\.3699\.1198\.21\+28\.5768\.7549\.11100\.0099\.11yesHyDE\-compatible∗62\.5075\.8997\.3298\.21\+35\.7164\.2951\.7998\.2197\.32yesRQ\-RAG\-compatible∗62\.5074\.1199\.1198\.21\+35\.7168\.7547\.32100\.0099\.11yesRAPTOR5\.3611\.6116\.9616\.07\+10\.717\.147\.14–16\.96no

Figure 5:Session\-level paired effects for the registered controlled interventions\. The vertical reference marks zero effect\.Panel B provides a preregistered 112\-session confirmation independent of the seven\-session implementation smoke\. Across the seven evaluated backends, PSS improves over the ambiguous raw query by 10\.71–35\.71 points\. BGE\-M3, Contriever, Qwen3\-Embedding\-4B, and compatible HyDE/RQ\-RAG pipelines satisfy the joint Holm\-corrected rule against raw, matched\-wrong, and shuffled states; their mean All\-Recall@3 rises from 65\.54% to 98\.75%\. BM25 and RAPTOR add gains of 18\.75 and 10\.71 points, respectively\. PSS also matches the parsed request reference within−0\.89\-0\.89to\+1\.79\+1\.79points without online history replay, establishing it as a portable intent layer for heterogeneous frozen retrieval systems\. Exact backend contracts and statistical gates are documented in[AppendicesO](https://arxiv.org/html/2610.33047#A15)and[F](https://arxiv.org/html/2610.33047#A6)\([Izacard et al\., 2021](https://arxiv.org/html/2610.33047#bib.bib15);[Gao et al\., 2023](https://arxiv.org/html/2610.33047#bib.bib9);[Chan et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib4);[Zhang et al\., 2025b](https://arxiv.org/html/2610.33047#bib.bib34);[Sarthi et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib27)\)\.

### 3\.4RQ2: Do functional outputs align with session\-specific intent?

Correct\-state clues move ambiguous queries toward their gold retrieval\-intent rewrites in the original 1,024\-dimensional BGE\-M3 space\. Relative to raw, matched\-wrong, and shuffled controls, session\-level target alignment improves by 0\.1136–0\.1779; every confidence interval is bounded away from zero and every Holm\-adjustedpp\-value is 0\.000300 \([Table3](https://arxiv.org/html/2610.33047#S3.T3)\)\.

Table 3:Session\-level functional\-output alignment effects aggregated over writer seeds 91–93 in the original 1,024\-dimensional BGE\-M3 space, with 95% stratified\-bootstrap CIs and Holm\-adjusted one\-sided sign\-flip tests\.CandidateReferenceEffect95% CIpHolmp\_\{\\mathrm\{Holm\}\}PSS clue retrievalAmbiguous raw query\+0\.1136\[\+0\.1008, \+0\.1266\]0\.000300PSS clue retrievalMatched\-wrong state\+0\.1227\[\+0\.1119, \+0\.1336\]0\.000300PSS clue retrievalShuffled state\+0\.1779\[\+0\.1646, \+0\.1907\]0\.000300Factorization\-invariant effective\-update fingerprints are not organized by the eight coarse semantic categories: cosine silhouette is−0\.0090\-0\.0090, and same\-category nearest\-neighbor frequency is 1\.17% versus a 12\.16% chance rate\. Thus the functional output is session\-specific even though this coarse taxonomy does not explain state proximity\. Because target alignment is encouraged by the retrieval\-clue objective, we interpret it as validation of the intended state function\. Full fingerprint construction, UMAPs, energy heatmaps, and analysis scope appear in[AppendicesC](https://arxiv.org/html/2610.33047#A3)and[F](https://arxiv.org/html/2610.33047#A6)\.

### 3\.5RQ3: Design interventions and ablations

The registered interventions confirm that full ordered history, session correspondence, and learned parameter structure each contribute to retrieval; PSS clue retrieval supplies the largest mechanism gain, while guarded use gives the best non\-oracle score \([Figure5](https://arxiv.org/html/2610.33047#S3.F5)\)\.

Table 4:Selected cross\-backbone RQ3 results\. Scores and effects are All\-Recall percentage points\. The canonical cell isr=32r\{=\}32,α=64\\alpha\{=\}64, last\-8, single\-slot\. Confirmation uses a disjoint 16\-session split and reports a 95% CI\.ModelCanonicalScreen selectionΔscreen\\Delta\_\{\\mathrm\{screen\}\}Δconfirm\\Delta\_\{\\mathrm\{confirm\}\}\[95% CI\]pHolmp\_\{\\mathrm\{Holm\}\}Qwen2\.5\-7B55\.00Last 16 layers\+17\.50\+7\.50 \[\-6\.25, \+21\.25\]0\.410Mistral\-7B79\.38Canonical retained\+0\.00——Phi\-3\-mini71\.88Last 16 layers\+6\.25\+7\.50 \[\+0\.00, \+17\.50\]0\.258Across Qwen, Mistral, and Phi\-3, the frozen rank\-32,α=64\\alpha\{=\}64, last\-8, single\-slot configuration remains the most reliable shared operating point\. Backbone\-specific screens reveal sensitivity to writer depth, rank, and slot count, while disjoint confirmation supports retaining the common configuration\. The complete intervention table, all screen cells, and the sensitivity figure appear in[AppendicesD](https://arxiv.org/html/2610.33047#A4)and[D\.1](https://arxiv.org/html/2610.33047#A4.SS1); frozen\-retriever and retrieval\-to\-QA extensions appear in[AppendicesO](https://arxiv.org/html/2610.33047#A15)and[G\.2](https://arxiv.org/html/2610.33047#A7.SS2)\.

#### History contribution and carrier choice\.

A preregistered three\-seed confirmation uses 320 independently generated PSS\-Carrier\-320 sessions \(40 per category\), disjoint from the original benchmark, development, and smoke\-test sessions\. Adding ordered history to a retrieval\-supervised PSS improves direct All\-Recall@4 over a target\-only PSS by 5\.54 points with BGE\-M3 and 10\.18 points with BM25; both effects survive Holm correction and remain positive for every writer seed\. Correct states also exceed matched\-wrong and shuffled states by 24\.05–39\.11 points\. Under dense semantic retrieval, PSS further exceeds a 256\-token persistent text memory with matched writer information and the reported wall\-clock write budget by 6\.25 points on this cohort\. A separate multi\-record experiment evaluates whether one compiled state can access different historical records in response to future questions\. AtK=16K=16, PSS reaches 83\.75% and 95\.00% All\-Recall@4 on BGE\-M3 and BM25, compared with 18\.75% and 35\.00% for all\-record concatenation and 16\.25% and 40\.00% for record\-wise RRF\. PSS attains the highest BGE\-M3 mean among the evaluated non\-reference methods; on BM25, Grok\-based selection reaches 97\.50%\. PSS performs this access through one local parameter\-conditioned generation and one evidence query, without supplying the text bank to the readout model\. Complete text\-access comparisons appear in[SectionV\.3](https://arxiv.org/html/2610.33047#A22.SS3);

## 4Related Work

#### Compact and parametric memory\.

Long\-context models retain historical tokens; StreamingLLM, Dynamic Memory Compression, SnapKV, and LongLLMLingua reduce their attention or prompt cost\([Li et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib20);[Jiang et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib17)\), while AutoCompressor, Gisting, ICAE, and Activation Beacon learn compact token or activation interfaces\([Chevalier et al\., 2023](https://arxiv.org/html/2610.33047#bib.bib6);[Mu et al\., 2023](https://arxiv.org/html/2610.33047#bib.bib23);[Ge et al\., 2023](https://arxiv.org/html/2610.33047#bib.bib10);[Zhang et al\., 2025a](https://arxiv.org/html/2610.33047#bib.bib32)\)\. LoRA provides a parameter\-efficient carrier\([Hu et al\., 2021](https://arxiv.org/html/2610.33047#bib.bib13)\); Deep Context Distillation, Cartridges, and Doc\-to\-LoRA internalize document or corpus content in parameter/KV modules\([Charakorn et al\., 2026](https://arxiv.org/html/2610.33047#bib.bib5)\)\. PSS instead uses one bounded LoRA state per session to recover retrieval scope after historical tokens disappear\. Exact facts remain external, and the state is unloaded before answering\.

#### RAG organization and query recovery\.

RAPTOR and HippoRAG organize evidence with hierarchical summaries or graphs\([Sarthi et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib27);[Gutiérrez et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib11)\)\. MemoRAG is closest in functional decomposition because memory generates clues before an expressive reader\([Qian et al\., 2025](https://arxiv.org/html/2610.33047#bib.bib26)\); PSS instead stores a per\-session parameter delta and tests it under ambiguous follow\-ups and wrong\-session interventions\. Conversational rewriters also bridge queries and evidence: CONQRR learns from retrieval rewards, IterCQR uses retrieval\-guided iteration, CHIQ enhances the history, AdaRewriter applies outcome\-supervised selection, and ConvSearch\-R1 uses retrieval\-aligned reinforcement learning\([Wu et al\., 2022](https://arxiv.org/html/2610.33047#bib.bib30);[Mo et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib22);[Lai et al\., 2025](https://arxiv.org/html/2610.33047#bib.bib18);[Zhu et al\., 2025](https://arxiv.org/html/2610.33047#bib.bib35)\)\. They normally reread textual dialogue online; PSS exposes a persistent textual clue interface without replaying that history\. Reproduction and checkpoint constraints for these baselines are reported in[SectionsG\.2](https://arxiv.org/html/2610.33047#A7.SS2)and[O](https://arxiv.org/html/2610.33047#A15)\.

#### Long\-term memory evaluation\.

Conversational rewriting and long\-term memory studies examine contextual query interpretation, indirectly expressed information, and cross\-session reasoning\([Wu et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib29);[Maharana et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib21)\)\. Our controlled protocols provide explicit session associations to the parameter writer and information\-matched text controls, allowing us to study compilation into parameters and subsequent retrieval use\. The public extension preserves LongBench and InfiniteBench source documents\([Bai et al\., 2024](https://arxiv.org/html/2610.33047#bib.bib2)\)while varying whether the query reveals its active request; PSS\-320 supports causal state interventions\.

## 5Conclusion

Underspecified follow\-ups expose a missing layer in conventional RAG: the retriever cannot search for session scope that the current query never states\. PSS fills this gap by compiling retrieval supervision and ordered history into a reusable parametric state that reconstructs what to search for without replaying historical tokens\. Across controlled sessions, public corpora, three language\-model families, and heterogeneous retrieval backends, correct states produce large, session\-attributable retrieval gains\. The controlled benchmark shows a 10\.63\-point gain over a compact card, and three\-seed carrier controls isolate ordered\-history information beyond supplied targets\. PSS therefore provides a retrieval\-scoped memory layer for repeated\-use assistants: compile session intent once, reuse it across RAG systems, and keep exact, versioned knowledge in an external, auditable evidence store\.

### AI use statement

Generative AI tools were used to assist with code development, text editing, and translation\. AI also contributed to drafting sections of the appendix and assisted in verifying certain datasets and results\.

### Ethics statement

PSS\-320 uses synthetic project names and controlled technical facts, with no human\-subject or private user data\.

### Reproducibility statement

[AppendicesB](https://arxiv.org/html/2610.33047#A2),[C](https://arxiv.org/html/2610.33047#A3),[G](https://arxiv.org/html/2610.33047#A7),[H](https://arxiv.org/html/2610.33047#A8),[E](https://arxiv.org/html/2610.33047#A5),[I](https://arxiv.org/html/2610.33047#A9),[J](https://arxiv.org/html/2610.33047#A10),[K](https://arxiv.org/html/2610.33047#A11),[S](https://arxiv.org/html/2610.33047#A19)and[T](https://arxiv.org/html/2610.33047#A20)document the experimental setup, data construction, controls, optimization, statistical analysis, and reproducibility details\.

## References

- Abdin et al\. \(2024\)Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, Alon Benhaim, Misha Bilenko, Johan Bjorck, Sébastien Bubeck, Martin Cai, Qin Cai, Vishrav Chaudhary, Dong Chen, Dongdong Chen, Weizhu Chen, Yen\-Chun Chen, Yi\-Ling Chen, Hao Cheng, Parul Chopra, Xiyang Dai, Matthew Dixon, Ronen Eldan, Victor Fragoso, Jianfeng Gao, Mei Gao, Min Gao, Amit Garg, Allie Del Giorno, Abhishek Goswami, Suriya Gunasekar, Emman Haider, Junheng Hao, Russell J\. Hewett, Wenxiang Hu, Jamie Huynh, Dan Iter, Sam Ade Jacobs, Mojan Javaheripi, Xin Jin, Nikos Karampatziakis, Piero Kauffmann, Mahoud Khademi, Dongwoo Kim, Young Jin Kim, Lev Kurilenko, James R\. Lee, Yin Tat Lee, Yuanzhi Li, Yunsheng Li, Chen Liang, Lars Liden, Xihui Lin, Zeqi Lin, Ce Liu, Liyuan Liu, Mengchen Liu, Weishung Liu, Xiaodong Liu, Chong Luo, Piyush Madan, Ali Mahmoudzadeh, David Majercak, Matt Mazzola, Caio César Teodoro Mendes, Arindam Mitra, Hardik Modi, Anh Nguyen, Brandon Norick, Barun Patra, Daniel Perez\-Becker, Thomas Portet, Reid Pryzant, Heyang Qin, Marko Radmilac, Liliang Ren, Gustavo de Rosa, Corby Rosset, Sambudha Roy, Olatunji Ruwase, Olli Saarikivi, Amin Saied, Adil Salim, Michael Santacroce, Shital Shah, Ning Shang, Hiteshi Sharma, Yelong Shen, Swadheen Shukla, Xia Song, Masahiro Tanaka, Andrea Tupini, Praneetha Vaddamanu, Chunyu Wang, Guanhua Wang, Lijuan Wang, Shuohang Wang, Xin Wang, Yu Wang, Rachel Ward, Wen Wen, Philipp Witte, Haiping Wu, Xiaoxia Wu, Michael Wyatt, Bin Xiao, Can Xu, Jiahang Xu, Weijian Xu, Jilong Xue, Sonali Yadav, Fan Yang, Jianwei Yang, Yifan Yang, Ziyi Yang, Donghan Yu, Lu Yuan, Chenruidong Zhang, Cyril Zhang, Jianwen Zhang, Li Lyna Zhang, Yi Zhang, Yue Zhang, Yunan Zhang, and Xiren Zhou\.Phi\-3 technical report: A highly capable language model locally on your phone, 2024\.URL[https://arxiv\.org/abs/2404\.14219](https://arxiv.org/abs/2404.14219)\.
- Bai et al\. \(2024\)Yushi Bai, Xin Lv, Jiajie Zhang, Hongchang Lyu, Jiankai Tang, Zhidian Huang, Zhengxiao Du, Xiao Liu, Aohan Zeng, Lei Hou, et al\.Longbench: A bilingual, multitask benchmark for long context understanding\.In*Proceedings of the 62nd annual meeting of the association for computational linguistics \(volume 1: Long papers\)*, pp\. 3119–3137, 2024\.
- Caccia et al\. \(2025\)Lucas Caccia, Alan Ansell, Edoardo Ponti, Ivan Vulić, and Alessandro Sordoni\.Training plug\-n\-play knowledge modules with deep context distillation\.*arXiv preprint arXiv:2503\.08727*, 2025\.
- Chan et al\. \(2024\)Chi\-Min Chan, Chunpu Xu, Ruibin Yuan, Hongyin Luo, Wei Xue, Yike Guo, and Jie Fu\.Rq\-rag: Learning to refine queries for retrieval augmented generation\.*arXiv preprint arXiv:2404\.00610*, 2024\.
- Charakorn et al\. \(2026\)Rujikorn Charakorn, Edoardo Cetin, Shinnosuke Uesaka, and Robert Tjarko Lange\.Doc\-to\-lora: Learning to instantly internalize contexts\.*arXiv preprint arXiv:2602\.15902*, 2026\.
- Chevalier et al\. \(2023\)Alexis Chevalier, Alexander Wettig, Anirudh Ajith, and Danqi Chen\.Adapting language models to compress contexts\.In*Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing*, pp\. 3829–3846, 2023\.
- Cormack et al\. \(2009\)Gordon V Cormack, Charles LA Clarke, and Stefan Buettcher\.Reciprocal rank fusion outperforms condorcet and individual rank learning methods\.In*Proceedings of the 32nd international ACM SIGIR conference on Research and development in information retrieval*, pp\. 758–759, 2009\.
- Eyuboglu et al\. \(2026\)Sabri Eyuboglu, Ryan Ehrlich, Simran Arora, Neel Guha, Dylan Zinsley, Emily Liu, Atri Rudra, James Y Zou, Azalia Mirhoseini, and Christopher Re\.Cartridges: Lightweight and general\-purpose long context representations via self\-study\.In*International Conference on Learning Representations*, volume 2026, pp\. 42642–42687, 2026\.
- Gao et al\. \(2023\)Luyu Gao, Xueguang Ma, Jimmy Lin, and Jamie Callan\.Precise zero\-shot dense retrieval without relevance labels\.In*Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\)*, pp\. 1762–1777, 2023\.
- Ge et al\. \(2023\)Tao Ge, Jing Hu, Lei Wang, Xun Wang, Si\-Qing Chen, and Furu Wei\.In\-context autoencoder for context compression in a large language model\.*arXiv preprint arXiv:2307\.06945*, 2023\.
- Gutiérrez et al\. \(2024\)Bernal J Gutiérrez, Yiheng Shu, Yu Gu, Michihiro Yasunaga, and Yu Su\.Hipporag: Neurobiologically inspired long\-term memory for large language models\.*Advances in neural information processing systems*, 37:59532–59569, 2024\.
- Holm \(1979\)Sture Holm\.A simple sequentially rejective multiple test procedure\.*Scandinavian journal of statistics*, pp\. 65–70, 1979\.
- Hu et al\. \(2021\)Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen\-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen\.Lora: Low\-rank adaptation of large language models\.*arXiv preprint arXiv:2106\.09685*, 2021\.
- Hui et al\. \(2024\)Binyuan Hui, Jian Yang, Zeyu Cui, Jiaxi Yang, Dayiheng Liu, Lei Zhang, Tianyu Liu, Jiajun Zhang, Bowen Yu, Keming Lu, et al\.Qwen2\. 5\-coder technical report\.*arXiv preprint arXiv:2409\.12186*, 2024\.
- Izacard et al\. \(2021\)Gautier Izacard, Mathilde Caron, Lucas Hosseini, Sebastian Riedel, Piotr Bojanowski, Armand Joulin, and Edouard Grave\.Unsupervised dense information retrieval with contrastive learning\.*arXiv preprint arXiv:2112\.09118*, 2021\.
- Jiang et al\. \(2023\)Albert Q\. Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, Lélio Renard Lavaud, Marie\-Anne Lachaux, Pierre Stock, Teven Le Scao, Thibaut Lavril, Thomas Wang, Timothée Lacroix, and William El Sayed\.Mistral 7b, 2023\.URL[https://arxiv\.org/abs/2310\.06825](https://arxiv.org/abs/2310.06825)\.
- Jiang et al\. \(2024\)Huiqiang Jiang, Qianhui Wu, Xufang Luo, Dongsheng Li, Chin\-Yew Lin, Yuqing Yang, and Lili Qiu\.Longllmlingua: Accelerating and enhancing llms in long context scenarios via prompt compression\.In*Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\)*, pp\. 1658–1677, 2024\.
- Lai et al\. \(2025\)Yilong Lai, Jialong Wu, Zhenglin Wang, and Deyu Zhou\.Adarewriter: unleashing the power of prompting\-based conversational query reformulation via test\-time adaptation\.In*Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing*, pp\. 3889–3905, 2025\.
- Lewis et al\. \(2020\)Patrick Lewis, Ethan Perez, Aleksandra Piktus, Fabio Petroni, Vladimir Karpukhin, Naman Goyal, Heinrich Küttler, Mike Lewis, Wen\-tau Yih, Tim Rocktäschel, et al\.Retrieval\-augmented generation for knowledge\-intensive nlp tasks\.*Advances in neural information processing systems*, 33:9459–9474, 2020\.
- Li et al\. \(2024\)Yuhong Li, Yingbing Huang, Bowen Yang, Bharat Venkitesh, Acyr Locatelli, Hanchen Ye, Tianle Cai, Patrick Lewis, and Deming Chen\.Snapkv: Llm knows what you are looking for before generation\.*Advances in Neural Information Processing Systems*, 37:22947–22970, 2024\.
- Maharana et al\. \(2024\)Adyasha Maharana, Dong\-Ho Lee, Sergey Tulyakov, Mohit Bansal, Francesco Barbieri, and Yuwei Fang\.Evaluating very long\-term conversational memory of llm agents\.In*Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\)*, pp\. 13851–13870, 2024\.
- Mo et al\. \(2024\)Fengran Mo, Abbas Ghaddar, Kelong Mao, Mehdi Rezagholizadeh, Boxing Chen, Qun Liu, and Jian\-Yun Nie\.Chiq: Contextual history enhancement for improving query rewriting in conversational search\.In*Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing*, pp\. 2253–2268, 2024\.
- Mu et al\. \(2023\)Jesse Mu, Xiang Li, and Noah Goodman\.Learning to compress prompts with gist tokens\.*Advances in Neural Information Processing Systems*, 36:19327–19352, 2023\.
- Multi\-Granularity \(2024\)Multi\-Linguality Multi\-Functionality Multi\-Granularity\.M3\-embedding: Multi\-linguality, multi\-functionality, multi\-granularity text embeddings through self\-knowledge distillation\.*arXiv preprint arXiv:2402\.03216*, 2024\.
- Nawrot et al\. \(2024\)Piotr Nawrot, Adrian Łańcucki, Marcin Chochowski, David Tarjan, and Edoardo M Ponti\.Dynamic memory compression: Retrofitting llms for accelerated inference\.*arXiv preprint arXiv:2403\.09636*, 2024\.
- Qian et al\. \(2025\)Hongjin Qian, Zheng Liu, Peitian Zhang, Kelong Mao, Defu Lian, Zhicheng Dou, and Tiejun Huang\.Memorag: Boosting long context processing with global memory\-enhanced retrieval augmentation\.In*Proceedings of the ACM on Web Conference 2025*, pp\. 2366–2377, 2025\.
- Sarthi et al\. \(2024\)Parth Sarthi, Salman Abdullah, Aditi Tuli, Shubh Khanna, Anna Goldie, and Christopher Manning\.Raptor: Recursive abstractive processing for tree\-organized retrieval\.In*International Conference on Learning Representations*, volume 2024, pp\. 32628–32649, 2024\.
- Tibshirani & Efron \(1993\)Robert J Tibshirani and Bradley Efron\.An introduction to the bootstrap\.*Monographs on statistics and applied probability*, 57\(1\):1–436, 1993\.
- Wu et al\. \(2024\)Di Wu, Hongwei Wang, Wenhao Yu, Yuwei Zhang, Kai\-Wei Chang, and Dong Yu\.Longmemeval: Benchmarking chat assistants on long\-term interactive memory\.*arXiv preprint arXiv:2410\.10813*, 2024\.
- Wu et al\. \(2022\)Zeqiu Wu, Yi Luan, Hannah Rashkin, David Reitter, Hannaneh Hajishirzi, Mari Ostendorf, and Gaurav Singh Tomar\.Conqrr: Conversational query rewriting for retrieval with reinforcement learning\.In*Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing*, pp\. 10000–10014, 2022\.
- Xiao et al\. \(2024\)Guangxuan Xiao, Yuandong Tian, Beidi Chen, Song Han, and Mike Lewis\.Efficient streaming language models with attention sinks\.In*International Conference on Learning Representations*, volume 2024, pp\. 21875–21895, 2024\.
- Zhang et al\. \(2025a\)Peitian Zhang, Zheng Liu, Shitao Xiao, Ninglu Shao, Qiwei Ye, and Zhicheng Dou\.Long context compression with activation beacon\.In*International Conference on Learning Representations*, volume 2025, pp\. 101932–101948, 2025a\.
- Zhang et al\. \(2024\)Xinrong Zhang, Yingfa Chen, Shengding Hu, Zihang Xu, Junhao Chen, Moo Khai Hao, Xu Han, Zhen Leng Thai, Shuo Wang, Zhiyuan Liu, et al\.∞\\inftybench: Extending long context evaluation beyond 100k tokens\.*arXiv preprint arXiv:2402\.13718*, 2024\.
- Zhang et al\. \(2025b\)Yanzhao Zhang, Mingxin Li, Dingkun Long, Xin Zhang, Huan Lin, Baosong Yang, Pengjun Xie, An Yang, Dayiheng Liu, Junyang Lin, et al\.Qwen3 embedding: Advancing text embedding and reranking through foundation models\.*arXiv preprint arXiv:2506\.05176*, 2025b\.
- Zhu et al\. \(2025\)Changtai Zhu, Siyin Wang, Ruijun Feng, Kai Song, and Xipeng Qiu\.Convsearch\-r1: Enhancing query reformulation for conversational search with reasoning via reinforcement learning\.In*Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing*, pp\. 26558–26575, 2025\.

## Appendix AFormal Task Contract and Algorithms

[Equation1](https://arxiv.org/html/2610.33047#S2.E1)separates the system into four stages so that the intervention and its outputs are unambiguous\. The writer changes only a session\-local adapter; online clue generation temporarily uses that adapter; retrieval uses an unchanged external index; and answering uses the unloaded, frozen base model\.[Table5](https://arxiv.org/html/2610.33047#A1.T5)records the information boundary at each stage\. The main paired comparison holds𝒟\\mathcal\{D\},RϕR\_\{\\phi\},kk, and the reader fixed while replacing only the query source: rawqsq\_\{s\}, a textual card, the correct PSS clue, a matched\-wrong clue, or a shuffled\-state clue\. Hence an evidence\-retrieval gain is attributable to recovered session intent rather than a different index, retriever, or answer model\. The retrieved chunk IDs and their order are additionally fixed in the answer\-stage ablation, isolating whether a loaded state contributes anything beyond retrieval\.

StageAvailable inputsMutable objectOutputExplicitly unavailableOffline writeOrderedHsH\_\{s\}, frozenθ\\theta, adapter contract𝒞θ\\mathcal\{C\}\_\{\\theta\}; clue supervision during trainingSession factorsΔs\\Delta\_\{s\}onlySerialized bounded stateΔs\\Delta\_\{s\}Formal answers and target\-document IDsOnline clueCurrentqsq\_\{s\},Δs\\Delta\_\{s\}, frozenθ\\thetaNoneclueq~s\\tilde\{q\}\_\{s\}Historical tokens and gold evidenceRetrievalq~s\\tilde\{q\}\_\{s\}, shared𝒟\\mathcal\{D\}, frozenRϕR\_\{\\phi\}NoneRanked evidenceEsE\_\{s\}Gold target labelsAnswerqsq\_\{s\}, retrievedEsE\_\{s\}, frozenpθp\_\{\\theta\}NoneFinal responseysy\_\{s\}HsH\_\{s\}and loadedΔs\\Delta\_\{s\}Table 5:Stage\-wise PSS information and mutation contract\.
## Appendix BExperimental Setup and Sessionization Details

### B\.1Evaluation rationale and method vocabulary

Our primary evaluation isolates the capability PSS is designed to provide: recovering retrieval\-critical session scope that is absent from the current query\. We remove those terms without placing answers in the writer input, hold the corpus, index, retriever, and reader fixed, and vary only the query source or session\-state condition\. Success therefore measures whether a reusable state enables an otherwise unchanged RAG pipeline to retrieve the intended evidence\.

We build a three\-layer evidence chain\. sessionizations of public tasks test transfer beyond the controlled domain\. PSS\-320 places many sessions in a shared candidate corpus and uses matched\-wrong, shuffled, zero, null, and OOD states to identify session\-specific effects\. Frozen\-retriever, cross\-backbone, and same\-evidence comparisons then test portability and localize the gain to retrieval\. Together, these experiments distinguish recovered session intent from generic query improvement or answer\-stage memorization\.

#### Stable method vocabulary\.

We use three names throughout the primary evaluations\.*PSS clue retrieval*loads the correct session state, emits an clue, and retrieves using that clue alone; it is the core mechanism\.*Raw \+ PSS RRF*is an unconditional fusion ablation of raw and PSS\-clue rankings\.*Guarded PSS*is the complete three\-way system whose router chooses raw, card, or PSS\-RRF\. Correct, wrong, shuffled, and zero identify causal state conditions rather than additional methods\. On the public transformation, the three\-way arm includes the parsed active\-request reference among its candidate actions\. Its transfer and safety analysis is consolidated in[AppendixF](https://arxiv.org/html/2610.33047#A6)\. The distinct\-record extension in[SectionV\.3](https://arxiv.org/html/2610.33047#A22.SS3)separately uses the original question concatenated with generated or selected retrieval text\.

Algorithm 1Offline compilation of one session stateFrozen base model

θ\\theta; adapter contract

𝒞θ\\mathcal\{C\}\_\{\\theta\}; ordered history

HsH\_\{s\}; positive and negative clue targets

\(zs\+,zs−\)\(z\_\{s\}^\{\+\},z\_\{s\}^\{\-\}\); state budget

BB; registered phase lengths

TLM,TreadT\_\{\\mathrm\{LM\}\},T\_\{\\mathrm\{read\}\}and learning rates

Serialized session state

Δs\\Delta\_\{s\}
Initialize LoRA factors

Δs\\Delta\_\{s\}permitted by

𝒞θ\\mathcal\{C\}\_\{\\theta\}; freeze all parameters in

θ\\theta
Split

HsH\_\{s\}into bounded chunks while preserving their original order

Initialize the LM\-phase optimizer on

Δs\\Delta\_\{s\}
for

t=1,…,TLMt=1,\\ldots,T\_\{\\mathrm\{LM\}\}do

xt←x\_\{t\}\\leftarrowthe next ordered history chunk

Update

Δs\\Delta\_\{s\}using

∇ΔsℒLM​\(xt,θ\+Δs\)\\nabla\_\{\\Delta\_\{s\}\}\\mathcal\{L\}\_\{\\mathrm\{LM\}\}\(x\_\{t\};\\theta\+\\Delta\_\{s\}\)
endfor

Retain

Δs\\Delta\_\{s\}; initialize a new readout\-phase optimizer

c0←c\_\{0\}\\leftarrowthe fixed session\-clue instruction

for

t=1,…,Treadt=1,\\ldots,T\_\{\\mathrm\{read\}\}do

ℓ\+←−logpθ\+Δs\(zs\+∣c0\)/\|zs\+\|\\ell\_\{\+\}\\leftarrow\-\\log p\_\{\\theta\+\\Delta\_\{s\}\}\(z\_\{s\}^\{\+\}\\mid c\_\{0\}\)/\|z\_\{s\}^\{\+\}\|

ℓ−←−logpθ\+Δs\(zs−∣c0\)/\|zs−\|\\ell\_\{\-\}\\leftarrow\-\\log p\_\{\\theta\+\\Delta\_\{s\}\}\(z\_\{s\}^\{\-\}\\mid c\_\{0\}\)/\|z\_\{s\}^\{\-\}\|

ℒread←ℓ\+\+max⁡\(0,m\+ℓ\+−ℓ−\)\\mathcal\{L\}\_\{\\mathrm\{read\}\}\\leftarrow\\ell\_\{\+\}\+\\max\(0,m\+\\ell\_\{\+\}\-\\ell\_\{\-\}\)

Update

Δs\\Delta\_\{s\}only using

∇Δsℒread\\nabla\_\{\\Delta\_\{s\}\}\\mathcal\{L\}\_\{\\mathrm\{read\}\}
endfor

Verify adapter topology, dtype, finite tensors, and

bytes⁡\(Δs\)≤B\\operatorname\{bytes\}\(\\Delta\_\{s\}\)\\leq B
Serialize

Δs\\Delta\_\{s\}with its model, writer, seed, and configuration metadata

return

Δs\\Delta\_\{s\}

Algorithm 2Online PSS clue retrieval and state\-isolated answeringCurrent query

qsq\_\{s\}; state

Δs\\Delta\_\{s\}; shared corpus

𝒟\\mathcal\{D\}; frozen retriever

RϕR\_\{\\phi\}; frozen base model

pθp\_\{\\theta\}; cutoff

kk; optional guard

gg
Retrieval clue

q~s\\tilde\{q\}\_\{s\}, evidence

EsE\_\{s\}, and response

ysy\_\{s\}
Temporarily load

Δs\\Delta\_\{s\}into the base model

q~s←Gθ\+Δs​\(qs\)\\tilde\{q\}\_\{s\}\\leftarrow G\_\{\\theta\+\\Delta\_\{s\}\}\(q\_\{s\}\)⊳\\trianglerightsearch clue

rPSS←Rϕ​\(q~s,𝒟\)r\_\{\\mathrm\{PSS\}\}\\leftarrow R\_\{\\phi\}\(\\tilde\{q\}\_\{s\},\\mathcal\{D\}\)

ifguard

ggis enabledthen

Compute raw and card rankings and deployment\-observable router features

as←g⁡\(qs,q~s,ranking features\)a\_\{s\}\\leftarrow g\(q\_\{s\},\\tilde\{q\}\_\{s\},\\text\{ranking features\}\)

Es←TopKkE\_\{s\}\\leftarrow\\operatorname\{TopK\}\_\{k\}of the raw, card, or raw–PSS RRF ranking selected by

asa\_\{s\}
else

Es←TopKk⁡\(rPSS\)E\_\{s\}\\leftarrow\\operatorname\{TopK\}\_\{k\}\(r\_\{\\mathrm\{PSS\}\}\)

endif

Unload

Δs\\Delta\_\{s\}and restore the frozen base model

θ\\theta
ys∼pθ​\(y∣qs,Es\)y\_\{s\}\\sim p\_\{\\theta\}\(y\\mid q\_\{s\},E\_\{s\}\)

return

\(q~s,Es,ys\)\(\\tilde\{q\}\_\{s\},E\_\{s\},y\_\{s\}\)

### B\.2Why session\-intent memory benefits from a different evaluation

#### The identification gap in conventional QA\.

A standard long\-context QA item gives the model an information\-sufficient question: the relevant entities, topic, relation, or time frame normally appear in the current input\. Such an item can measure document retrieval and reading, but it does not test the failure mode in[Figure1](https://arxiv.org/html/2610.33047#S1.F1)\. A retriever may succeed without recovering any session state because the query already says what to search for\. Conversely, an end\-to\-end answer score does not reveal whether a failure arose from interpreting the session, retrieving evidence, or decoding the answer\. Merely prepending more history also changes the online token budget and gives a long\-context model direct access to the very information that a persistent memory is supposed to recover\.

#### Conditions for causal identification\.

The claim tested byPSSis narrower and causal: given an underspecified follow\-up, does the state written from sessionssrestore the missing retrieval intent of that same session? Our evaluation instantiates the following conditions\. First, the online query omits decisive project, entity, relation, or version terms while remaining resolvable from the ordered history\. Second, the writer has no access to the answer, gold document ID, or evaluation label\. Third, test sessions retrieve from a shared, locked candidate corpus; choosing a separate index for each session would reveal the active project before the query is interpreted\. Fourth, correct\-state results are paired with matched\-wrong, shuffled, and zero\-state controls, reducing the chance that a generic rewrite or regularization effect is mistaken for session memory\. Finally, null, OOD, revision, and conflict probes expose false activation and stale\-scope failures, while session\-disjoint splits and session\-level inference prevent probes from the same history from being treated as independent evidence\.

PropertyConventional QAPublic sessionizationPSS\-320Current queryUsually self\-containedambiguous follow\-upControlled ambiguous and compositional probesCandidate corpusTask document\(s\)Released public documentsShared locked corpus across test sessionsPrimary attributionRetrieval plus readingCorrect vs\. wrong/shuffled sessionCorrect vs\. wrong/shuffled/zero stateRobustness probesRarely explicitNull and OOD variantsNull/OOD, revision, and conflict variantsMain roleGeneral task performanceExternal validityCausal mechanism identificationTable 6:Evaluation roles and identification conditions\. All PSS writer inputs exclude answers and target\-document identifiers\.
#### Why two complementary tracks are retained\.

sessionizations of released benchmarks preserve real source documents, established metrics, and cross\-domain variation, but some instances remain easy or reach single\-document ceilings\. PSS\-320 supplies the missing experimental control: balanced ambiguity types, revision structure, evidence groups, causal state interventions, and a shared cross\-session retrieval pool\. It is therefore used to identify the session\-intent mechanism rather than to replace public benchmark evaluation\. The public and controlled tracks answer different questions—whether the method transfers to released data, and whether its gains are specifically caused by recovering the corresponding session’s omitted intent\. Construction, human\-audit, and leakage\-check details appear in[AppendicesI](https://arxiv.org/html/2610.33047#A9)and[S](https://arxiv.org/html/2610.33047#A19)\.

### B\.3Benchmarks and sessionization

#### Public sessionized ambiguity\.

We derive 326 sessions from the QA portions of NarrativeQA, Qasper, MultiFieldQA\-en, HotpotQA, 2WikiMQA, MuSiQue, and InfiniteBench En\.QA\. Each history contains up to four released queries and marks one as active; the online input is a fixed underspecified continuation\. Documents, answers, and target IDs are hidden from the writer\. Seed fixes 32 guard\-fit, 32 confirmation, and 262 sealed\-test sessions before core evaluation\. Every session has correct, same\-task wrong\-history, shuffled\-history, null, and OOD variants; the audited run writes all 652 required states with zero failures\. Retrieval uses BGE\-M3 and target\-document All\-Recall@3\. The*parsed active\-request reference*deterministically extracts and persists the complete request designated by the history’s activity marker\. It can be executed when these explicit markers are available and serves as a text reference with resolved request selection\. The same request supplies PSS’s positive readout target\. Both paths therefore receive explicit request associations: this protocol evaluates retrieval access under shared supervision, rather than intent identification in unmarked natural conversations\. This reference is distinct from the compact structured card used on PSS\-320\.

#### UltraDomain\.

A separate 112\-session transformation tests transfer to finance, legal, and miscellaneous documents\. The original released QA task contains no session history, so PSS is inapplicable; long\-context and BGE\-M3 results on the released task are descriptive references reported in[AppendixH](https://arxiv.org/html/2610.33047#A8)\.

#### Controlled sessions \(PSS\-320\)\.

Public document QA is externally grounded but can become easy after sessionization\. We therefore use PSS\-320, 320 AI\-controlled synthetic technical\-project sessions and 1,920 probes\. We reserve 64 sessions for state/router development and report a source\-group\-disjoint test of 256 sessions \(1,536 probes\)\. Each test session contains canonical, paraphrase, anaphora, composition, exact\-fact, and null/conflict probes and specifies every evidence group needed for success\. The generator balances eight semantic categories and multiple history lengths, topic counts, revisions, and relation depths\. Automated audits verify split disjointness, unique answers, and evidence alignment\. A completed stratified human comparison additionally checks history coherence, intended scope, evidence sufficiency, null validity, and exclusion of formal\-answer supervision\. Because these sessions remain synthetic, PSS\-320 is a controlled mechanism benchmark; the construction contract is in[AppendixI](https://arxiv.org/html/2610.33047#A9)\.

### B\.4Models, controls, and evaluation

Before portability evaluation, we froze the writer objective, rank, topology, precision, splits, comparisons, and multiplicity families\. Qwen2\.5\-7B, Mistral\-7B, and Phi\-3\-mini each write architecture\-specific states; no tensor is shared across models\. The primary study uses Qwen2\.5\-7B\-Instruct in BF16 with greedy decoding, BM25, 192\-token chunks, andk=4k=4; interaction studies add BGE\-small, BGE\-M3, summary\-leaf, and entity\-relation retrieval\. Baselines include raw query, recent context, structured card, summary, full\-history rewrite, Raw \+ PSS RRF, ConvSearch\-R1, gold query/evidence, and capped full context\. Every state\-bearing arm receives correct, matched\-wrong, parameter\-shuffled, and zero states\. The answer ablation holds the query, retrieved chunk IDs, and chunk order fixed while varying only the decoding state\.[AppendicesM](https://arxiv.org/html/2610.33047#A13)and[P](https://arxiv.org/html/2610.33047#A16)lists every arm and diagnostic\.

Calibration selected a retrieval\-aligned, rank\-32, single\-slot, full\-ordered\-history BF16 state\. The primary PSS\-320 result tables, together with the state\-fingerprint, functional\-alignment, and Qwen query\-bank diagnostics, aggregate the independent H200 writer runs with seeds 91–93 under the same frozen configuration and controls\. The Mistral/Phi portability, 112\-session strong\-backend confirmation, 320\-session carrier confirmation, and public transfer runs likewise report writer seeds 91–93 under their separate frozen registrations; results are not pooled across protocols\. We retain the session, rather than probes or query variants, as the unit of inference\. The primary endpoints are evidence All\-Recall@4 on PSS\-320 and target\-document All\-Recall@3 on public data\. Statistical reporting uses paired category\-stratified bootstrap intervals with 10,000 resamples, exact McNemar or sign\-flip tests as registered, and Holm correction\. A dagger is generated only when all registered positive comparisons against declared baselines have Holm\-adjustedp<0\.05p<0\.05; complete gates and deviations appear in[AppendicesL](https://arxiv.org/html/2610.33047#A12)and[S](https://arxiv.org/html/2610.33047#A19)\.

For visual reporting, tables use neutral backgrounds and script\-computed bold and underline for best and second\-best performance\. RQ1 figures use blue for PSS clue/fusion arms, orange for the guarded system or router diagnostics, and gray for baselines and controls\. Color indicates experimental role rather than statistical significance\.

![Refer to caption](https://arxiv.org/html/2610.33047v1/pss_state_geometry.png)Figure 6:Factorization\-invariant geometry for 256 held\-out sessions, aggregated over independently written Qwen PSS updates from writer seeds 91–93: descriptive UMAP and median effective\-update energy heatmaps\.#### State\-geometry result\.

In the preregistered effective\-update fingerprint space, the category cosine silhouette is \-0\.0090\. The nearest neighbor shares its semantic category for 1\.17% of sessions, versus a 12\.16% finite\-sample chance rate \(enrichment \-10\.98 points; 10,000\-label\-permutationp=1p=1\)\. These statistics are computed before UMAP projection;[Figure6](https://arxiv.org/html/2610.33047#A2.F6)is descriptive\.

## Appendix CState Fingerprints and Functional\-Output Alignment

Raw LoRAA/BA/Bentries are not identifiable because rescalingAAand inversely rescalingBBleaves the effective update unchanged\. We therefore preregister a factorization\-invariant analysis of the 256 correct Qwen states\. For each layer–module pair, we compute∥B​A∥F2=tr⁡\(B⊤​B​A​A⊤\)\\lVert BA\\rVert\_\{F\}^\{2\}=\\mathrm\{tr\}\(B^\{\\top\}BAA^\{\\top\}\)and deterministic Rademacher projectionsu⊤​B​A​vu^\{\\top\}BAv\. The standardized projections form a state fingerprint\. Category silhouette and same\-category nearest\-neighbor enrichment are evaluated before projection with a 10,000\-label\-permutation test; two\-dimensional UMAP is used only for visualization\. Layer–module and category–module heatmaps report median within\-state energy shares\.

The functional\-alignment follow\-up was frozen only after observing the coarse\-category clustering null\. BGE\-M3 embeds the raw query, the clue produced by the correct state, matched\-wrong and shuffled\-state clues, and the gold retrieval\-intent rewrite\. The gold rewrite is an evaluation target only; neither answer strings nor answer predictions enter the analysis\. Primary comparisons are session\-level averages over five answerable probes, tested with one\-sided sign flips and Holm correction\. All effects are computed in the original 1,024\-dimensional space rather than in UMAP\. Since the state is trained with a retrieval\-clue objective, these tests validate output behavior and session specificity; they are not an intrinsic probe of relational parameter geometry\.

Figure 7:Generated\-clue trajectories and target\-alignment effects\. UMAP is descriptive; effects are computed in the original 1,024\-dimensional BGE\-M3 space\.#### Registered functional\-output alignment follow\-up\.

Motivated by the frozen coarse\-category clustering null, we measured whether the clue generated by a state moves an ambiguous query toward its gold retrieval\-intent rewrite\. Across 256 sessions and writer seeds 91–93, PSS\-clue progress over raw was \+0\.1136 \(95% CI \[\+0\.1008, \+0\.1266\]; Holmp=0\.00029997p=0\.00029997\)\. PSS\-clue progress exceeded matched\-wrong and shuffled controls by \+0\.1227 and \+0\.1779, respectively \(Holmp=0\.00029997p=0\.00029997andp=0\.00029997p=0\.00029997\)\. All tests aggregate writer seeds before session\-level inference; answers and answer predictions are not used\. These effects validate session\-specific output alignment, not relational geometry of the underlying parameters\.

## Appendix DDesign Intervention Summary

Table 7:Registered design interventions on PSS\-320\. Effects are absolute All\-Recall@4 differences except for the answer\-F1 row\.Design questionTreatment / controlEffectInterpretationUse full ordered history?Full\-history / query\-only writer\+0\.1188History contributes beyond the active request \(n=32n=32\)✓\\checkmarkSession\-specific state?PSS clue / matched wrong\+0\.1750Session identity matters✓\\checkmarkLearned parameter structure?PSS clue / shuffled\+0\.1211Not explained by equal\-sized parameter loading✓\\checkmarkGuard clue use?Guarded PSS / PSS clue\+0\.0055Best non\-oracle score; PSS\-320 null/OOD activation is 0\.78%Fuse unconditionally?PSS clue / Raw \+ PSS RRF\+0\.1297PSS clue ranking is stronger than unconditional fusionKeep state for answering?Keep state / unload state\+0\.0037 F1Retrieval\-first deployment uses the unload path### D\.1Cross\-backbone hyperparameter sensitivity

#### Writer and state design\.

Calibration first selected the retrieval\-aligned objective, then preregistered a 32\-session one\-factor\-at\-a\-time screen over rank, LoRA scale, write depth, and slot topology\. All other factors remain fixed to full\-history BF16, and the canonical cell isr=32r\{=\}32,α=64\\alpha\{=\}64, last 8 layers, and one slot\.[Figure8](https://arxiv.org/html/2610.33047#A4.F8)reports percentage\-point changes in All\-Recall@4 rather than cumulative bridge totals, because effects from different cells cannot be added\.

#### Backbone\-specific parameter effects\.

Qwen is the most capacity\-sensitive: relative to its 55\.00% canonical score,r=64r\{=\}64,α=128\\alpha\{=\}128, and last\-16 writing gain 12\.50, 16\.25, and 17\.50 points on the screen\. The last\-16 winner, however, yields only\+7\.50\+7\.50points on the disjoint 16\-session confirmation set \(95% CI\[−6\.25,21\.25\]\[\-6\.25,21\.25\], Holmp=0\.410p\{=\}0\.410\)\. Mistral behaves differently: its 79\.38% canonical cell wins, and every tested change is lower;r=16r\{=\}16,r=64r\{=\}64, and last\-16 each lose 6\.88–8\.12 points\. Phi is less sensitive to rank and scale \(\+0\.62\+0\.62forr=16r\{=\}16,\+2\.50\+2\.50forr=64r\{=\}64, and\+1\.88\+1\.88forα=128\\alpha\{=\}128\), while last\-16 wins the screen by 6\.25 points and confirms at\+7\.50\+7\.50points \(95% CI\[0\.00,17\.50\]\[0\.00,17\.50\], Holmp=0\.258p\{=\}0\.258\)\. These profiles show that PSS supports backbone\-specific tuning while the locked canonical cell remains a robust shared configuration across all three models\.

#### Capacity, placement, and topology\.

The cross\-model pattern is non\-monotone\. Doubling rank helps Qwen and only slightly helps Phi, but harms Mistral; increasingα\\alphais a zero\-storage change that helps Qwen strongly, helps Phi modestly, and harms Mistral\. Writing the last 16 layers doubles state size and is selected for Qwen and Phi, but not for Mistral\. A capacity\-controlled second slot never improves the canonical cell: dual\-r=16r\{=\}16loses 20\.00, 2\.50, and 8\.75 points for Qwen, Mistral, and Phi, respectively\. The result strongly supports the locked single\-slot topology, whose canonical state sizes are 44, 40, and 24 MiB per session\. Additional semantic\-peak analysis appears in[AppendixQ](https://arxiv.org/html/2610.33047#A17)\.

Figure 8:Three\-backbone, one\-factor\-at\-a\-time sensitivity around the lockedr=32r\{=\}32,α=64\\alpha\{=\}64, last\-8, single\-slot configuration, with a disjoint confirmation set for the screen\-selected cell\.

## Appendix ESupervision and Carrier Confirmation

This preregistered follow\-up tests whether ordered history contributes beyond the canonical target supplied to the writer and whether parameters offer utility beyond persistent text produced offline from the same information\. It uses the newly generated PSS\-Carrier\-320 confirmation cohort \(320 sessions; 40 per category\), created after and disjoint from the original PSS\-320 benchmark and all development and smoke\-test sessions\. It includes all answerable probes, BGE\-M3\([Multi\-Granularity, 2024](https://arxiv.org/html/2610.33047#bib.bib24)\)and BM25, and writer seeds 91–93\. All histories fit the registered 16K window; the audit passes every split, seed, compute\-matching, and coverage check\.

The matched state receives\(Hs,zs\+,zs−\)\(H\_\{s\},z\_\{s\}^\{\+\},z\_\{s\}^\{\-\}\); the target\-only state omitsHsH\_\{s\}\. The strongest text baseline uses the same history, supervision, offline model family, 256\-token budget, and matched per\-session generation compute\. Neither method replays history online\. Direct retrieval is primary; a guard fitted outside the confirmation sessions supplies the secondary view\.

Table 8:Information\-by\-carrier confirmation \(session\-weighted All\-Recall@4, percent\)\. Retriever cells report direct/guarded retrieval\. “Null act\.” is frozen\-guard null/OOD activation\.ArmBGE\-M3BM25Null act\.Raw query12\.50/12\.5017\.32/17\.320\.00Direct target17\.50/16\.4341\.96/34\.1179\.46Direct target pair17\.32/17\.8638\.39/30\.8933\.93Text from history, 32 tokens11\.79/13\.7531\.25/26\.0783\.48Text from history, 128 tokens13\.93/14\.6439\.46/29\.4685\.71Text from history, 256 tokens15\.36/15\.5442\.14/30\.8985\.71Text from\(H,z\)\(H,z\), 32 tokens11\.07/13\.0434\.46/25\.8978\.57Text from\(H,z\)\(H,z\), 128 tokens16\.43/16\.9638\.21/29\.2980\.80Text from\(H,z\)\(H,z\), 256 tokens21\.25/19\.4653\.04/38\.5783\.93Compute\-matched text from\(H,z\)\(H,z\)21\.07/20\.0053\.39/38\.3982\.59PSS from history only4\.64/9\.6416\.07/19\.4685\.71PSS from target only21\.79/21\.6132\.14/27\.3242\.41PSS from\(H,z\)\(H,z\), correct27\.32/21\.0742\.32/31\.0717\.86PSS from\(H,z\)\(H,z\), wrong0\.36/11\.253\.21/14\.8217\.41PSS from\(H,z\)\(H,z\), shuffled3\.27/9\.4015\.18/16\.8597\.17Table 9:Preregistered direct\-retrieval effects in percentage points\. Holm correction is within the registered family; “all seeds” requires a common direction across the three writer seeds\.RetrieverComparisonEffect95% CIHolmppAll seedsBGE\-M3history increment\+5\.54\[\+0\.36,\+10\.71\+0\.36,\+10\.71\]0\.0428yesBGE\-M3PSS−\-matched text\+6\.25\[\+1\.25,\+11\.43\+1\.25,\+11\.43\]0\.0346yesBGE\-M3correct−\-wrong\+26\.96\[\+22\.32,\+31\.79\+22\.32,\+31\.79\]<10−4<10^\{\-4\}yesBGE\-M3correct−\-shuffled\+24\.05\[\+19\.17,\+28\.81\+19\.17,\+28\.81\]<10−4<10^\{\-4\}yesBM25history increment\+10\.18\[\+3\.93,\+16\.61\+3\.93,\+16\.61\]0\.0051yesBM25PSS−\-matched text−11\.07\-11\.07\[−18\.04,−4\.11\-18\.04,\-4\.11\]0\.9990noBM25correct−\-wrong\+39\.11\[\+33\.39,\+44\.82\+33\.39,\+44\.82\]<10−4<10^\{\-4\}yesBM25correct−\-shuffled\+27\.14\[\+21\.55,\+32\.80\+21\.55,\+32\.80\]<10−4<10^\{\-4\}yesHistory increment is positive after correction for both retrievers and every seed, showing thatHsH\_\{s\}contributes beyond\(zs\+,zs−\)\(z\_\{s\}^\{\+\},z\_\{s\}^\{\-\}\)\. The carrier effect is representation\-dependent: PSS beats matched text with BGE\-M3, while BM25 favors lexically richer text\. Large correct–wrong and correct–shuffled margins rule out arbitrary\-adapter and generic\-rewrite explanations\. The frozen guard exceeds its 5% null/OOD threshold \(17\.86% for correct PSS\), so its transfer gate fails\. We do not tune on the confirmation set; direct retrieval remains the registered primary analysis\.

## Appendix FLimitations and Threats to Validity

This section consolidates the scope qualifications for the performance claims in the main paper\. In particular, it records the distinction between retrieval and answer decoding, router\-transfer behavior, UltraDomain ceiling effects, cost relative to textual state, backend implementation status, benchmark construction, and privacy or continual\-learning questions\. These limitations do not change the registered retrieval improvements; they define the settings to which those improvements can currently be generalized\.

### F\.1Experimental status

The selected writer configuration, controls, and decision rules are fixed across writer seeds 91–93\. All reported PSS\-320 values and diagnostics aggregate these seeds while retaining sessions as the independent units for paired inference, including when seed runs were executed on separate machines\. The Mistral, Phi\-3, UltraDomain, and 112\-session strong\-backend protocols were frozen before their respective reported comparisons, providing separate portability and backend confirmations\. The carrier confirmation in[AppendixE](https://arxiv.org/html/2610.33047#A5)uses the newly generated, disjoint PSS\-Carrier\-320 cohort and the same writer seeds 91–93 to test history increment and a text baseline under the reported wall\-clock budget and a separate preregistration\.

### F\.2Synthetic benchmark and sampled human audit

PSS\-320 is generated from controlled templates with model\-assisted text realization and programmatic evidence alignment\. This supports causal interventions and exact evidence groups, but also introduces repeated linguistic patterns, artificial identifiers, and a narrow technical\-project domain\. The completed 32\-session stratified review compares sampled histories, scope\-resolving rewrites, supporting evidence, null probes, and the separation between writer targets and formal answers\. It provides a human check on the benchmark’s construction and labels\.

The public extension reduces dependence on that generator \. Histories contain released source questions plus an explicit request\-ordinal control turn\. En\.QA and NarrativeQA sessions each index one shared document and therefore saturate target\-document recall for nearly every arm\.

UltraDomain adds domain diversity but not natural dialogue\. Its sessionized raw arm already reaches 94\.64–96\.43%, and none of the three models passes the preregistered joint support threshold\. Correct PSS states nevertheless raise All\-Recall@3 over raw by 1\.79–4\.46 points for every backbone; the “no” support flags record the threshold decision, not an absence of retrieval benefit\. The original released QA task is useful for long\-context and retrieval baselines but does not evaluate PSS because it contains no session history\.

### F\.3Router transfer across domains

The 32\-session public router chooses only raw or parsed\-reference actions and never the PSS\-RRF action on the 262\-session sealed test\. Although it improves over raw retrieval, it reduces recall relative to PSS clue retrieval and activates on 11\.83% of null and 25\.57% of OOD probes\. The corresponding confirmation rates, 3\.13% and 34\.38%, also show unstable OOD behavior\. The 0\.78% conditional activation reported on PSS\-320 therefore does not provide a portable safety guarantee\. The independently frozen guard in the carrier confirmation likewise misses its registered 5% transfer gate: correct\-PSS null/OOD activation is 17\.86%, and routing reduces both BGE\-M3 and BM25 retrieval relative to the direct primary analysis\. We do not retune either threshold on its test set\. A deployable guard may benefit from larger, more diverse negative data and a separately frozen cross\-domain evaluation\.

### F\.4Separation of retrieval and answer generation

The primary endpoint is evidence retrieval, not answer correctness\. All answer arms have zero Exact Match, and even gold\-query and capped\-full\-context controls reach only about 0\.35 token F1\. These controls isolate the demonstrated contribution to evidence access; reader optimization is outside the retrieval intervention evaluated here\.

### F\.5State capacity and scaling

The state has fixed shape for one session, but the experiment does not prove that it preserves all information in the session\. The writer is explicitly optimized for session fields and retrieval clues, and retention is expected to degrade when useful information exceeds its finite capacity\. Write compute grows linearly with history chunks\. Storage grows linearly in the number of sessions, and current query, retrieved text, and generated\-token KV still consume online memory\. Hence “zero history tokens” is not “zero tokens”, “zero memory”, or an asymptotic constant\-memory system over arbitrarily many sessions\.

### F\.6Cost relative to text state

The primary Qwen rank\-32 state occupies 44\.04 MiB and takes 29\.03 seconds to write; audited logical sizes are 44, 40, and 24 MiB for Qwen, Mistral, and Phi\-3\. The sealed parsed request averages 65\.65 raw UTF\-8 bytes\. Text cards therefore optimize storage, editability, and write latency, while PSS targets retrieval utility through a reusable non\-text carrier\. The public parsed reference provides the stronger retrieval/F1 trade\-off, and Equationmakes positive held\-out utility, reuse\.

With identical history and target information, the same offline model family, a 256\-token text budget, and matched per\-session generation compute, PSS gains 6\.25 points under BGE\-M3, while BM25 gains 11\.07 points from lexically explicit text\.

### F\.7Retriever and domain interaction

BM25 is unusually strong because PSS\-320 contains project IDs, version strings, configuration names, and checkpoint identifiers\. Dense BGE\-small performs poorly on the generated clues, whereas BGE\-M3 improves substantially when paired with the same state rewrite\. The graph\-compatible result also transfers, but its performance depends on the entity\-extraction, graph\-construction, community\-summarization, and retrieval configurations, as well as their indexing cost\. Likewise, the 112\-session HyDE\- and RQ\-RAG\-compatible rows freeze their query\-transformation logic around the common retriever contract; they are not official end\-to\-end reproductions of those systems\. These are model/data interactions, not a general ranking of lexical, dense, hierarchical, and graph retrieval\. Natural paraphrases, multilingual sessions, and semantically equivalent descriptions could change the result\.

### F\.8Capped context and efficiency scope

The primary PSS\-320 full\-context input is capped at 32,768 tokens\. Nominal 65K histories are therefore truncated and the arm is not a true full\-history oracle\. Original UltraDomain uses different declared context regimes: Qwen is YaRN\-compatible, Mistral is native\-32K truncated, and Phi\-3 is native\-128K; their Full rows are consequently not a controlled backbone ranking\. Efficiency uses 16 sessions and one measured generation length; it does not report run\-to\-run standard deviation, energy, validated FLOPs, or all length\-specific curves\. The 67\.64% latency and 11\.60% peak\-allocation reductions are descriptive for the measured hardware/software state, not universal system constants\.

### F\.9Qualitative and capacity\-analysis scope

Only 42 of 240 semantic\-peak combinations yield identifiable breakpoints\. The observed breakpoints are therefore reported descriptively and do not identify a capacity law or a globally optimal rank\.

### F\.10Privacy, deletion, and continual learning

Per\-session adapters can retain sensitive information\. Correct/wrong/shuffled controls do not test membership inference, source extraction, adapter theft, unlearning, or deletion\. The registry experiment does not demonstrate continual learning, non\-interference across sequential updates, or rollback\. Deployment considerations include access control, encryption, lifecycle management, and privacy testing\.

### F\.11Threats by validity class

#### Internal validity\.

The active query and clue are available to some writer objectives, so query\-only and target\-only controls are important\. The three\-seed carrier confirmation shows that adding history improves over the target\-only state for both registered retrievers, but its history\-only state remains below raw\. This supports retrieval\-supervised history integration\. Matched\-wrong states are balanced by category and difficulty but do not match every lexical property\. The sequential calibration can create researcher degrees of freedom\. Aggregating the locked configuration over seeds 91–93, together with the separately frozen cross\-model and strong\-backend studies, reduces but does not eliminate this concern\.

#### Construct validity\.

Rewrite F1 is not retrieval success; retrieval success is not reader success; state bytes are not source compression ratio; and a fixed adapter shape is not evidence of losslessness\. Likewise, clue\-to\-target progress is close to the retrieval\-clue training objective: it validates functional output alignment but does not reveal relational geometry in parameter space\. We therefore prioritize all\-support evidence recall, report answer controls separately, and avoid generic “context compression” or intrinsic\-geometry claims\.

#### External validity\.

Seven public QA tasks, UltraDomain, two additional retrievers, and three backbones broaden the original synthetic\-domain result\. They establish method\-level portability across the tested adapter layouts, not direct reuse of one state across models\. One language, three tested writer seeds per state\-writing evaluation, three related decoder\-only model families\.

#### Statistical conclusion validity\.

H1/H2 have paired intervals and corrected tests, but H3 control gaps lack a complete per\-control interval table in the current artifact summary\. All reported state\-writing analyses aggregate seeds 91–93; category, semantic\-peak, and efficiency analyses remain exploratory where indicated\. Public and cross\-retriever sign\-flip tests use session\-level pairs and Holm correction, but their minimum reported Monte Carlopp\-value is1/\(100,000\+1\)1/\(100\{,\}000\+1\); it is not an exact value below that resolution\. Cross\-model tables preserve the preregistered Holm pass/fail decisions; they do not infer daggers from rounded aggregate means\. Original UltraDomain has no joint paired all\-method family; sessionized UltraDomain yields positive gains for every model without crossing the joint support threshold\.

## Appendix GPublic Sessionized Extension

### G\.1Per\-task retrieval and answering

Table 10:Sealed public target\-document All\-Recall@3 \(percent\)\. “PSS\-RRF” fuses raw and PSS\-clue rankings\. The final row is session\-weighted\. “Parsed ref\.” denotes the protocol\-resolved active\-request reference: the complete request designated by the history’s activity marker and used directly for retrieval\.TasknnRawFullZeroWrongShuffledPSS\-RRFPSS clueRouter diag\.Parsed ref\.2WikiMQA4030\.0062\.5052\.5042\.5022\.5095\.00100\.0072\.50100\.00HotpotQA4045\.0057\.5027\.5047\.5015\.0097\.50100\.0082\.50100\.00∞\\inftyBench En\.QA56100\.00100\.00100\.00100\.00100\.00100\.00100\.00100\.00100\.00MultiFieldQA\-en3053\.3363\.3360\.0066\.6736\.6793\.33100\.0073\.33100\.00MuSiQue4045\.0080\.0050\.0045\.0020\.0097\.50100\.0097\.50100\.00NarrativeQA16100\.00100\.00100\.00100\.00100\.00100\.00100\.00100\.00100\.00Qasper4057\.5070\.0067\.5062\.5052\.5082\.5077\.5077\.5080\.00Session\-weighted26260\.6975\.9564\.5065\.2748\.4795\.0496\.5686\.2696\.95

Table 11:Public answer token F1 \(percent\) after unloading the state\.Method2WikiHotpotEn\.QAMultiFieldMuSiQueNarrativeQasperWeightedRaw0\.120\.460\.752\.160\.112\.652\.301\.03Full\-history rewrite5\.852\.121\.1210\.131\.445\.912\.393\.56PSS clue retrieval31\.7424\.538\.5843\.1710\.3711\.9215\.2220\.00Router diagnostic30\.0221\.252\.3619\.7610\.618\.6515\.0015\.03Parsed ref\.37\.3325\.986\.7342\.4810\.0612\.5522\.9621\.78

The answer results are auxiliary because the primary intervention targets retrieval\. Unlike the earlier PSS\-320 reader diagnostic, public Exact Match is not universally zero; nevertheless, the generated aggregate currently reports only F1 in the paper table\. PSS\-clue F1 is 20\.00%, close to the parsed reference’s 21\.78% and well above the ambiguous query’s 1\.03%, under the strict answer isolation boundary\.

### G\.2Conversational\-rewrite retrieval\-to\-QA extension

The follow\-up registration was written before its formal run, and the completed artifact passed the independent matrix audit\. Its primary track reuses the locked 262\-session public sealed split; sessionized UltraDomain provides a separate 112\-session replication\. Both tracks forbid answers, documents, and target IDs from every rewriter\. Raw, parsed\-reference, and PSS rewrites are joined with an official Apache\-2\.0 ConvSearch\-R1 Qwen2\.5\-3B checkpoint trained on QReCC \. We retain the official history/rewrite prompt and temperature 0\.7; this is explicitly cross\-domain inference, not retraining on our sessionization\. One generated rewrite is shared by all three readers\. IterCQR has an official repository and Google Drive model release, but the released QReCC is a 66,322,432\-byte truncated PyTorch zip with no central\-directory record; the listed full\-size TopiOCQA asset has not yet passed integrity and reuse\-authorization checks\. CHIQ releases code but no checkpoint or observed license\. AdaRewriter’s README displays an MIT badge, but the inspected revision has no license file and no complete released candidate\-generator/reward checkpoint\. Exact rows for these methods therefore require complete author\-released predictions or a complete checkpoint with an explicit authorization record; unavailable methods receive no invented score\.

For every method, BGE\-M3 revision retrieves the same 512\-token, 64\-token\-overlap evidence interface at top\-3\. History is kept hidden and PSS is unloaded\. For the primary QA endpoint, the answer model receives one method\-invariant explicit source question plus method\-retrieved chunks, while the method rewrite is hidden; therefore answer differences isolate the downstream value of retrieved evidence\. We report rewrite\-plus\-evidence deployment QA secondarily\. Qwen2\.5\-7B, Mistral\-7B, and Phi\-3\-mini decode greedily in BF16\. The two primary endpoints are target\-document All\-Recall@3 and answer F1 on both public sessionizations\. We first average withinbase\_session\_id, then use paired two\-sided sign\-flip tests, paired 10,000\-sample session bootstraps, and one Holm family per track across reader, method, and endpoint, including every method–raw contrast and every PSS–baseline contrast\. We do not combine the two track\-levelpp\-values\. We declare a reliable retrieval\-to\-QA bridge against raw only when both retrieval and F1 effects against raw are positive after correction\. A paper\-table dagger is stricter and denotes positive endpoints against every declared baseline in that track’s family\. Cross\-dataset statements are reserved for cases in which both tracks pass independently\. The retrieval\-rescued subset is descriptive and is not called a mediation test\. The tables below retain positive mean changes that miss the adjusted threshold, but label them as descriptive rather than significant; negative results are reported without suppression\.

#### Outcome summary\.

On the primary public sessionized track, PSS passes the registered retrieval\-to\-QA criterion against the ambiguous raw query for all three readers: All\-Recall@3 rises by 35\.50–35\.88 points and controlled answer F1 rises by 4\.06–10\.60 points \(allpHolm=3\.0×10−4p\_\{\\mathrm\{Holm\}\}=3\.0\\times 10^\{\-4\}\)\. PSS also significantly exceeds ConvSearch\-R1 in retrieval by 14\.89–15\.27 points for every backbone, while its F1 advantage is significant only for Qwen2\.5\-7B\.

Sessionized UltraDomain exhibits a retrieval ceiling: PSS improves the mean All\-Recall@3 contrast against raw by 1\.79 points, but the adjusted retrieval test is nonsignificant\. Controlled answer F1 nevertheless improves by 10\.63–18\.69 points for all readers \(pHolm=3\.0×10−4p\_\{\\mathrm\{Holm\}\}=3\.0\\times 10^\{\-4\}\)\. We report these positive means and significant F1 effects, but do not relabel the track as passing the registered joint criterion\.

Figure 9:Session\-level paired retrieval and controlled\-answer effects on the public and UltraDomain sessionizations; whiskers are paired 95% bootstrap CIs\.ReaderMethodR@3Ctrl F1Ctrl EMDeploy F1Deploy EMQwen2\.5\-7BAmbiguous raw query60\.694\.620\.381\.310\.00Qwen2\.5\-7BParsed ref\.96\.9514\.962\.6715\.252\.67Qwen2\.5\-7BConvSearch\-R181\.3011\.742\.676\.800\.38Qwen2\.5\-7BPSS clue retrieval96\.5615\.223\.0515\.002\.29Mistral\-7BAmbiguous raw query60\.696\.540\.002\.340\.00Mistral\-7BParsed ref\.96\.9511\.320\.0011\.240\.00Mistral\-7BConvSearch\-R181\.3010\.020\.006\.350\.00Mistral\-7BPSS clue retrieval96\.1810\.600\.0011\.070\.00Phi\-3\-miniAmbiguous raw query60\.698\.610\.002\.380\.00Phi\-3\-miniParsed ref\.96\.9516\.031\.5316\.081\.53Phi\-3\-miniConvSearch\-R181\.3011\.810\.766\.600\.38Phi\-3\-miniPSS clue retrieval96\.5613\.441\.1512\.980\.76Table 12:Complete Public sessionized retrieval\-to\-QA results \(percent\)\. Ctrl uses the method\-invariant source question and method\-retrieved evidence; Deploy exposes each method rewrite\. Grok\-based recParsed ref\. denotes the complete active\-request text selected by the protocol’s explicit activity marker and used directly for retrieval\.ord selectionReaderPSS vs\.Δ\\DeltaR@3 \[95% CI\]pHolmp\_\{\\mathrm\{Holm\}\}Δ\\DeltaCtrl F1 \[95% CI\]pHolmp\_\{\\mathrm\{Holm\}\}Joint\+Qwen2\.5\-7Braw query\+35\.88 \[\+29\.77, \+42\.37\]3\.00e\-04\+10\.60 \[\+7\.93, \+13\.42\]3\.00e\-04yesQwen2\.5\-7BConvSearch\-R1\+15\.27 \[\+11\.07, \+19\.85\]3\.00e\-04\+3\.48 \[\+1\.51, \+5\.57\]0\.006yesQwen2\.5\-7BParsed ref\.\-0\.38 \[\-2\.67, \+1\.91\]1\.000\+0\.26 \[\-1\.98, \+2\.56\]1\.000noMistral\-7Braw query\+35\.50 \[\+29\.01, \+41\.98\]3\.00e\-04\+4\.06 \[\+2\.47, \+5\.74\]3\.00e\-04yesMistral\-7BConvSearch\-R1\+14\.89 \[\+10\.69, \+19\.47\]3\.00e\-04\+0\.58 \[\-0\.83, \+2\.00\]1\.000noMistral\-7BParsed ref\.\-0\.76 \[\-3\.05, \+1\.53\]1\.000\-0\.71 \[\-1\.85, \+0\.35\]1\.000noPhi\-3\-miniraw query\+35\.88 \[\+29\.39, \+42\.37\]3\.00e\-04\+4\.83 \[\+2\.77, \+6\.93\]3\.00e\-04yesPhi\-3\-miniConvSearch\-R1\+15\.27 \[\+10\.69, \+19\.85\]3\.00e\-04\+1\.62 \[\-0\.17, \+3\.54\]0\.619noPhi\-3\-miniParsed ref\.\-0\.38 \[\-2\.29, \+1\.53\]1\.000\-2\.59 \[\-4\.48, \-0\.89\]0\.029noTable 13:Complete Public sessionized session\-level PSS contrasts in percentage points, with paired 10,000\-sample bootstrap CIs and Holm\-adjusted tests\. Joint\+requires both effects to be positive with adjustedp<0\.05p<0\.05\.ReaderMethodR@3Ctrl F1Ctrl EMDeploy F1Deploy EMQwen2\.5\-7BAmbiguous raw query96\.4321\.700\.008\.590\.00Qwen2\.5\-7BParsed ref\.99\.1143\.660\.0044\.550\.00Qwen2\.5\-7BConvSearch\-R195\.5436\.270\.0032\.460\.00Qwen2\.5\-7BPSS clue retrieval98\.2140\.380\.0039\.500\.00Mistral\-7BAmbiguous raw query96\.4327\.200\.0013\.740\.00Mistral\-7BParsed ref\.99\.1143\.000\.0042\.720\.00Mistral\-7BConvSearch\-R195\.5435\.720\.0033\.350\.00Mistral\-7BPSS clue retrieval98\.2139\.360\.0039\.350\.00Phi\-3\-miniAmbiguous raw query96\.4330\.280\.0014\.860\.00Phi\-3\-miniParsed ref\.99\.1143\.580\.0043\.940\.00Phi\-3\-miniConvSearch\-R195\.5439\.840\.0032\.680\.00Phi\-3\-miniPSS clue retrieval98\.2140\.920\.0038\.590\.00Table 14:Complete Sessionized UltraDomain retrieval\-to\-QA results \(percent\)\. Ctrl uses the method\-invariant source question and method\-retrieved evidence; Deploy exposes each method rewrite\. Grok\-based recParsed ref\. denotes the complete active\-request text selected by the protocol’s explicit activity marker and used directly for retrieval\.ord selectionReaderPSS vs\.Δ\\DeltaR@3 \[95% CI\]pHolmp\_\{\\mathrm\{Holm\}\}Δ\\DeltaCtrl F1 \[95% CI\]pHolmp\_\{\\mathrm\{Holm\}\}Joint\+Qwen2\.5\-7Braw query\+1\.79 \[\-2\.68, \+6\.25\]1\.000\+18\.68 \[\+14\.41, \+22\.81\]3\.00e\-04noQwen2\.5\-7BConvSearch\-R1\+2\.68 \[\+0\.00, \+6\.25\]1\.000\+4\.11 \[\+0\.72, \+7\.45\]0\.335noQwen2\.5\-7BParsed ref\.\-0\.89 \[\-2\.68, \+0\.00\]1\.000\-3\.28 \[\-6\.24, \-0\.44\]0\.519noMistral\-7Braw query\+1\.79 \[\-2\.68, \+6\.25\]1\.000\+12\.16 \[\+9\.00, \+15\.26\]3\.00e\-04noMistral\-7BConvSearch\-R1\+2\.68 \[\+0\.00, \+6\.25\]1\.000\+3\.64 \[\+1\.37, \+5\.90\]0\.044noMistral\-7BParsed ref\.\-0\.89 \[\-2\.68, \+0\.00\]1\.000\-3\.64 \[\-6\.18, \-1\.19\]0\.095noPhi\-3\-miniraw query\+1\.79 \[\-2\.68, \+6\.25\]1\.000\+10\.63 \[\+7\.51, \+13\.65\]3\.00e\-04noPhi\-3\-miniConvSearch\-R1\+2\.68 \[\+0\.00, \+6\.25\]1\.000\+1\.08 \[\-1\.76, \+3\.91\]1\.000noPhi\-3\-miniParsed ref\.\-0\.89 \[\-2\.68, \+0\.00\]1\.000\-2\.67 \[\-6\.01, \+0\.51\]1\.000noTable 15:Complete Sessionized UltraDomain session\-level PSS contrasts in percentage points, with paired 10,000\-sample bootstrap CIs and Holm\-adjusted tests\. Joint\+requires both effects to be positive with adjustedp<0\.05p<0\.05\.
#### Interpretation boundary\.

These results separate two claims\. First, PSS reliably restores omitted session intent on the primary public sessionization\. Second, positive mean changes below the registered threshold remain descriptive and are retained in the figure and complete tables; they are not promoted to significant retrieval\-to\-QA support\. Accordingly, no dagger is assigned in this extension and no cross\-track combinedpp\-value is constructed\.

### G\.3Paired effects, controls, and audit

Table 16:Public sealed\-test paired All\-Recall@3 effects\. Tests are two\-sided session\-level sign flips with a single Holm family of six comparisons\.ComparisonDifferencepppHolmp\_\{\\mathrm\{Holm\}\}PSS clue−\-raw\+0\.35889\.9999×10−69\.9999\{\\times\}10^\{\-6\}5\.99994×10−55\.99994\{\\times\}10^\{\-5\}PSS clue−\-wrong\+0\.31309\.9999×10−69\.9999\{\\times\}10^\{\-6\}5\.99994×10−55\.99994\{\\times\}10^\{\-5\}PSS clue−\-shuffled\+0\.48099\.9999×10−69\.9999\{\\times\}10^\{\-6\}5\.99994×10−55\.99994\{\\times\}10^\{\-5\}Router diagnostic−\-raw\+0\.25579\.9999×10−69\.9999\{\\times\}10^\{\-6\}5\.99994×10−55\.99994\{\\times\}10^\{\-5\}Router diagnostic−\-Parsed ref\.\-0\.10691\.99998×10−51\.99998\{\\times\}10^\{\-5\}5\.99994×10−55\.99994\{\\times\}10^\{\-5\}Router diagnostic−\-full rewrite\+0\.10310\.0016100\.001610The reporting script assigns no dagger to the public method because its rule is satisfied only when the public router diagnostic significantly surpasses raw, the parsed reference, and full history; the reference comparison has a negative effect\. For the PSS\-320 retriever interaction, the four state\-versus\-raw/card comparisons each use 256 paired sessions and havepHolm=3\.99996×10−5p\_\{\\mathrm\{Holm\}\}=3\.99996\\times 10^\{\-5\}, so both state rows in[Table2](https://arxiv.org/html/2610.33047#S3.T2)receive a dagger\.

Table 17:Public null/OOD false activation \(percent\)\. Unguarded output is non\-abstaining for every probe\.SplitProbePSS clueRouter diag\.Confirmation \(n=32n=32\)Null100\.003\.13Confirmation \(n=32n=32\)OOD100\.0034\.38Sealed test \(n=262n=262\)Null100\.0011\.83Sealed test \(n=262n=262\)OOD100\.0025\.57The final aggregate contains 4,192 rows for 262/262 expected sessions\. The state audit covers three write shards, 652 states, zero failures, and no shard outside the registered failure tolerance\. On sealed answerable sessions the router chooses the parsed reference 158 times and raw 104 times, with zero PSS\-RRF choices\. These counts explain why the guard improves abstention while sacrificing much of the correct\-state retrieval gain\.

## Appendix HCross\-Model and UltraDomain Details

Table 18:Full cross\-model control matrix \(percent target\-document All\-Recall@3\)\. Public and UltraDomain are separate sessionized protocols\. “Support” applies the preregistered positive, Holm\-corrected comparisons of the PSS clue produced by the correct state against raw, wrong, and shuffled controls\. The router diagnostic includes the parsed\-reference action\.ModelTracknnRawWrongShuffledPSS clueRouter diag\.Parsed ref\.SupportQwen2\.5\-7BPublic26260\.6965\.2748\.4796\.5686\.2696\.95yesMistral\-7BPublic26261\.8362\.2147\.7195\.8083\.2198\.09yesPhi\-3\-miniPublic26260\.6963\.3648\.0995\.8085\.1197\.33yesQwen2\.5\-7BUltra sessionized11296\.4390\.1889\.2998\.2199\.1199\.11noMistral\-7BUltra sessionized11294\.6491\.9687\.5098\.2198\.2199\.11noPhi\-3\-miniUltra sessionized11294\.6491\.0788\.3999\.1198\.2199\.11no

The public correct–wrong gaps are 31\.30, 33\.59, and 32\.44 points, and the correct–shuffled gaps are 48\.09, 48\.09, and 47\.71 points for Qwen, Mistral, and Phi\-3\. These matched controls rule out a generic benefit from loading any adapter\. UltraDomain’s direction is also consistent, but the high raw and parsed\-reference ceilings prevent the complete preregistered decision from passing\.

Table 19:Original released UltraDomain QA \(normalized token F1, percent\)\. PSS is N/A because no session history is provided\. Qwen is YaRN\-compatible, Mistral is explicitly 32K\-truncated, and Phi\-3 is native 128K\. Formatting is script\-generated; no dagger is emitted because there is no joint paired all\-method test artifact\.ModelFamilyMethodFinLegalMisc \(Mix\)Ave\.Qwen2\.5\-7BLong contextYaRN\-compatible46\.8650\.1647\.6648\.23Qwen2\.5\-7BRetrievalBGE\-M344\.9645\.3547\.8746\.06Mistral\-7BLong contextNative\-32K truncated42\.2638\.9744\.5441\.92Mistral\-7BRetrievalBGE\-M345\.8744\.0446\.2345\.38Phi\-3\-miniLong contextNative\-128K51\.1746\.5248\.0948\.59Phi\-3\-miniRetrievalBGE\-M345\.7745\.4747\.4346\.22

Phi\-3 native\-128K obtains the best average \(48\.59\), narrowly ahead of Qwen’s YaRN\-compatible 48\.23\. BGE\-M3 beats Mistral’s truncated long\-context path by 3\.46 points, whereas long context beats BGE\-M3 by 2\.17 points for Qwen and 2\.37 points for Phi\-3\. These are descriptive comparisons across unequal context budgets; original UltraDomain evaluates long\-context QA, not PSS\.

Table 20:Audited model\-state contracts\. Logical state size is measured from the actual BF16 state manifest; every model has zero write failures\. Context labels describe the original UltraDomain long\-context baseline, not the PSS writer’s 128\-token chunks\.ModelRevisionLong\-context labelLoRA targetsLayersMiB/sessionQwen2\.5\-7BmainYaRN\-compatible 128Kq,k,v,o,gate,up,downfinal 844Mistral\-7Bb3af163native 32K, truncatedq,k,v,o,gate,up,downfinal 840Phi\-3\-minif3c06aednative 128Kqkv,o,gate\-up,downfinal 824

The smallest state, Phi\-3’s 24 MiB snapshot, obtains the strongest PSS\-320 scores in both added retrievers\. This is an efficiency observation, not a causal architecture claim: hidden size, fused projections, backbone quality, and state parameter count change together\. The experiment establishes method\-level portability, not cross\-model interchangeability of state files\.

## Appendix IPSS\-320 Construction and Audit

### I\.1Generation contract

Each session describes one synthetic technical project\. The generator first samples a semantic category and a balanced combination of load factors\. It then instantiates:

1. 1\.an active project, topic, component, configuration, and current decision;
2. 2\.archived same\-type alternatives and, where applicable, superseded decisions;
3. 3\.one to eight source documents containing the controlled evidence;
4. 4\.an ordered session history containing the evidence plus routine distractor turns;
5. 5\.a 32\-token structured card, a 128\-token summary, and writer fields;
6. 6\.six evaluation probes, gold rewrites, answer strings, and one or more required evidence groups\.

The history and source documents use independent surface realizations of the same controlled facts\. Formal probe answers are serialized only in the evaluation records and are prohibited from writer input\. The source is released under CC0\-1\.0\.

### I\.2Splits and balance

Table 21:PSS\-320 split and calibration roles\.PartitionSessionsProbesRoleCalibration–selection32192writer/rank/topology selectionCalibration–guard fit1696feature scaling and router fitCalibration–confirmation1696threshold/risk confirmationHeld\-out test2561536aggregate over writer seeds 91–93Total3201920Every semantic category contains eight calibration and 32 test sessions\. Each of the four levels of every load axis appears in 16 calibration and 64 test sessions\. Source\-group IDs are disjoint across calibration and test\. Both are retained to distinguish the source records from the prepared experiment representation\.

### I\.3Probe definitions

Table 22:Six probes instantiated for every session\.ProbeIntended capabilityCanonical readoutRecover an explicitly recorded active request\.Unseen paraphraseResolve a new surface form of an existing intent\.Anaphoric queryResolve references such as “that configuration”\.New compositionRetrieve all groups in a relation chain not stated as one sentence\.Exact factLocate versions, dates, thresholds, and checkpoints\.Null/conflictReject out\-of\-scope or superseded requests\.The first three probes diagnose session\-scope recovery\. New composition and exact fact stress evidence access rather than free\-form parametric recall\. Null/conflict probes have empty evidence groups and a gold rewrite of UNSUPPORTED\.

### I\.4Evidence and leakage audit

For answerable probes, each evidence group contains one or more text spans that jointly support one component of the answer\. All\-Recall@4 equals one only when at least one chunk from every group is present in the top four\. Automated checks enforce: 320 unique sessions; 1,920 probes; balanced category/axis counts; source\-group split disjointness; unique formal answer strings; and no formal answer use by the writer\. All automated issues are zero\.

The human audit samples one calibration and three test sessions from each category\. Reviewers compare each sampled record with its history, intended scope, evidence groups, null status, and writer target to check history coherence, scope resolution, evidence sufficiency, null validity, and formal\-answer exclusion\. The completed 32\-session comparison provides sampled human validation of these construction criteria\.

## Appendix JWriter Training and State Construction

### J\.1Backbone and adapter placement

The backbone is Qwen2\.5\-7B\-Instruct in BF16\. LoRA is inserted intoq\_proj,k\_proj,v\_proj,o\_proj,gate\_proj,up\_proj, anddown\_projin the final eight transformer layers\. The selected state has rank 32 andα/r=2\\alpha/r=2\. Only the state parameters are optimized; the backbone remains frozen\.

### J\.2Language\-model phase

The selected history coverage isfull\_ordered\_history\. Tokenized history is divided into 128\-token chunks\. The number of LM updates ismax⁡\(16,Nchunks\)\\max\(16,N\_\{\\mathrm\{chunks\}\}\), ensuring every chunk is visited at least once\. Optimization uses AdamW, learning rate2×10−52\\times 10^\{\-5\}, no weight decay, and gradient clipping at 1\.0\. Activations are bounded by the chunk size, but total write time increases with the number of chunks\.

### J\.3Retrieval\-aligned readout

After the LM phase, the selectedretrieval\_alignedimplementation uses 64 updates at learning rate10−410^\{\-4\}: the sum of the configured 32 readout and 32 retrieval steps\. Every update in this phase uses the loss in[Equation4](https://arxiv.org/html/2610.33047#S2.E4), with a newly initialized phase optimizer\. Its positive target is a compact clue containing the project, current configuration/component, checkpoint, and route terms\. The hard negative uses a same\-session archived configuration or unrestricted answer path\. The margin in[Equation4](https://arxiv.org/html/2610.33047#S2.E4)is 0\.2\. Training excludes the evaluation probe answer\.

### J\.4Writer objective screen

Table 23:Writer objectives in the registered screen\.ObjectiveTraining signalLM\-onlyOrdered\-history next\-token modeling\.Query\-onlyCanonical active\-query readout; no history LM\.LM \+ queryHistory LM plus active\-query readout\.Multi\-fieldTopic, entities, latest decision, and query readout\.Retrieval\-alignedHistory LM plus positive clue over hard\-negative margin\.Multi\-field \+ retrievalMulti\-field targets plus retrieval alignment\.The final lock choseretrieval\_aligned; this differs from the base configuration file’s original rank\-4multi\_field\_plus\_retrievaldefault\. The run artifact, not the unmodified default, is the source of truth for the reported method\.

### J\.5History and content ablations

The history\-coverage matrix contains active query only, last 128 tokens, first 25/50/75%, full ordered history, full history with shuffled chunk order, and structured card only\. Content deletion separately removes active query, active topic, entities, key evidence, latest decision, or superseded decision\. These interventions distinguish query caching, bag\-of\-facts retention, order sensitivity, and version handling\.

### J\.6Capacity, topology, and precision

The registered ranks are 2, 4, 8, 16, and 32 with fixedα/r\\alpha/r\. Topologies are a single slot and a dual slot intended to separate stable document state from writable session state\. Precision arms are BF16 full snapshot, BF16 base plus FP16 residual, INT8 residual, and INT4 residual\. The final lock is rank 32, single slot, BF16 full snapshot\. The semantic\-peak stage does not establish rank 32 as globally optimal \([AppendixQ](https://arxiv.org/html/2610.33047#A17)\)\.

### J\.7Causal states

For each test session we construct four states:

- •correct:written from that session;
- •matched wrong:written from another session matched by category and difficulty;
- •shuffled:the correct state’s parameter values are permuted within the registered control transformation;
- •zero reset:the initial no\-write state\.

All controls use the same backbone, prompts, retriever, and scoring code\.

## Appendix KRouter Features, Cross\-Fitting, and Fallback

### K\.1Feature set

The first 11 features compare raw and PSS\-clue paths:

1. 1\.explicit state refusal;
2. 2\.raw/rewrite Jaccard similarity;
3. 3\.raw\-query containment in the rewrite;
4. 4\.rewrite novelty;
5. 5\.raw/PSS top\-4 chunk overlap;
6. 6\.raw/PSS top\-1 agreement;
7. 7\.normalized PSS top\-1 versus top\-2 margin;
8. 8\.normalized PSS versus raw top\-score gain;
9. 9\.raw\-query overlap with raw evidence;
10. 10\.raw\-query overlap with state\-retrieved evidence;
11. 11\.PSS\-clue overlap with PSS\-retrieved evidence\.

The three\-way router adds the analogous refusal, similarity, novelty, ranking, score, and evidence\-overlap features for the card path, plus state/card top\-4 overlap and top\-1 agreement\. All text overlap is computed over normalized lexical tokens\.UNSUPPORTED,UNANSWERABLE,NO ANSWER, andINSUFFICIENT EVIDENCEare explicit refusals\.

### K\.2Model fitting

The router contains one balanced logistic scope model and one logistic reward model per action \(raw,card, and the implementation keystate\_rrf, reported as PSS\-RRF\)\. Feature means and scales are learned on calibration data only\. Four\-fold memory\-level cross\-fitting ensures that a session does not both fit a model and produce its own out\-of\-fold threshold prediction\. The scope threshold and action margins are fixed before test evaluation\. A low scope score selects the raw action\. Otherwise, the highest adjusted action score wins, with raw preferred on exact ties\.

### K\.3Information boundary

Permitted features use only the current raw query, generated rewrites, retrieved chunk IDs/scores, and text overlap with returned chunks\. The router is not given access to the session ID, probe ID, semantic category, state\-control label, gold evidence, formal answer, or test outcome\. The state writer and router calibration both complete before held\-out evaluation\.

### K\.4Why three actions are retained

The raw path protects literal or out\-of\-scope questions\. The card provides a cheap and interpretable global\-theme summary\. PSS\-RRF can recover fine\-grained project/configuration terms absent from both\. The final test routes 518 probes to raw, 472 to card, and 546 to PSS\-RRF\. These counts show non\-degenerate use of all three paths, but action\-conditioned accuracy is selected and therefore not a causal estimate of action quality\.

### K\.5RRF implementation

For each candidate chunk, the implementation sums reciprocal ranks from the raw and PSS\-clue lists with constant 60, sorts by decreasing fused score and stable chunk ID, and keeps the first four\. No learned reranker is used\. Raw \+ PSS RRF is an unconditional fusion ablation; the formal PSS\-RRF action is selected by the Guarded PSS router\.

## Appendix LRegistered Questions, Gates, and Deviations

Table 24:Registered hypotheses and observed decisions\.HypothesisGateResultH1 raw superiorityΔ​A​l​l−R​e​c​a​l​l​@​4≥0\.10\\Delta All\-Recall@4\{\}\\geq 0\.10and CI lower\>0\>0Pass:\+0\.3328\+0\.3328H2 card non\-inferiorityCI lower≥−0\.02\\geq\-0\.02Pass; actually\+0\.1117\+0\.1117H3 causal bindingcorrect–wrong and correct–shuffled≥0\.10\\geq 0\.10Pass:\+0\.1750,\+0\.1211\+0\.1750,\+0\.1211H4 full\-history semanticsfull history–query only≥0\.05\\geq 0\.05Mechanism pass:\+0\.1188\+0\.1188H5 answer combinationcorrect exceeds unload, wrong, shuffled by 0\.05Fail; unload gap\+0\.0037\+0\.0037Null/OODconditional false activation≤0\.05\\leq 0\.05Pass: 0\.0078Failuremaximum arm failure rate≤0\.02\\leq 0\.02Pass: 0### L\.1Registered research questions

The protocol asks whether the state supports zero\-history retrieval, whether it contains more than an active\-query cache, whether it improves complete evidence retrieval, whether keeping it active improves answering, where semantic capacity fails, and when its cost is preferable to a text card\. H1–H5 map these questions to explicit effect\-size gates\.

### L\.2Sequential calibration design

The original full factorial would require six objectives, five ranks, two topologies, and three seeds\. The revised design first screens six objectives at ranks 4/8 with a single slot, then screens rank and topology only for the selected objective\. This estimates the principal objective effect in the pilot\-supported rank range and a selected\-objective capacity/topology curve; it does not estimate every objective\-by\-rank\-by\-topology interaction\.

### L\.3Evaluation status and claim scope

The selected configuration is evaluated with writer seeds 91, 92, and 93 on H200 hardware\. The same frozen configuration, controls, and decision rules are used for every seed, and seed\-level evidence is summarized before reporting\. Thus, passing H1–H4 and the safety gates reflects replication across initializations\. Claim scope remains limited by synthetic session construction, mechanical public sessionization, and the reader and router limitations reported elsewhere\.

The automated report contains an internalcontext\_compression\_claim\_allowed=trueflag because H4 passes its mechanism threshold\. The top\-level report correctly leavesparameterized\_context\_compression\_supported=false\. We follow the top\-level interpretation in this paper\.

## Appendix MComplete Arm Definitions and Aggregate Retrieval Results

Table 25:Thirteen main arms\. History tokens denote the configured online history\-derived text budget, including cards and summaries\. Guarded PSS includes its card branch\. “Unload” means that the LoRA state is removed before answer generation\.ArmHistory tokensRetrieval and answer pathRaw0Raw ambiguous query; base 7B \+ RAG\.Recent\-128128Recent\-window rewrite; base 7B \+ RAG\.Card\-3232Structured\-card rewrite; base 7B \+ RAG\.Summary\-128128Text\-summary rewrite; base 7B \+ RAG\.Full sessionfullFull\-history rewrite; base 7B \+ RAG\.PSS clue, unload0PSS clue retrieval; unload; base 7B \+ RAG\.Guarded PSS, unload32 \(card\)Raw/card/PSS\-RRF routing; unload; base 7B \+ RAG\.PSS clue, keep0PSS clue retrieval; keep selected answer state \+ RAG\.Guarded PSS, keep32 \(card\)Guarded query/evidence; keep answer state \+ RAG\.PSS clue \+ card32PSS and card hybrid rewrite; unload \+ RAG\.Gold query0Canonical query; base 7B \+ RAG\.Gold evidence0Gold evidence groups; base 7B answer\.Full contextfullCapped history, no retrieval; base 7B answer\.Table 26:Aggregate retrieval diagnostics\. History tokens denote the configured online history\-derived text budget; Guarded PSS includes its card branch\. Actual prompt\-token and full\-path cost measurements are reported separately in[SectionV\.5](https://arxiv.org/html/2610.33047#A22.SS5)\.PathHistory tokensAll\-Recall@4Difference from rawRaw query00\.1734–Recent\-1281280\.1359\-0\.0375Card\-32320\.3945\+0\.2211Summary\-1281280\.4023\+0\.2289Full\-session rewritefull0\.3578\+0\.1844PSS clue retrieval00\.5008\+0\.3273Raw \+ PSS RRF00\.3711\+0\.1977Guarded PSS32 \(card\)0\.5063\+0\.3328Gold query00\.8281\+0\.6547### M\.1State controls

For the guarded arm, correct, matched\-wrong, and shuffled states obtain 0\.5063, 0\.3313, and 0\.3852 All\-Recall@4\. The equal\-sized four\-control summary implies an approximate zero\-reset value of 0\.3867; we treat this absolute number as provisional pending regeneration from per\-control rows\. The registered causal decisions depend on the directly reported correct–wrong and correct–shuffled gaps, not the reconstructed zero value\.

## Appendix NSemantic Category Analysis

Table 27:BM25 retrieval diagnostic by semantic category\. This table uses PSS clue retrieval with the correct state to isolate clue quality; it is not the Guarded PSS router’s category\-conditioned performance\.CategoryRawCardPSS cluePSS−\-RawPSS−\-CardActive topic0\.21880\.38750\.4813\+0\.2625\+0\.0938Coreference0\.15000\.36250\.5375\+0\.3875\+0\.1750Entity binding0\.15630\.36250\.5000\+0\.3438\+0\.1375Exact fact0\.15630\.36250\.5250\+0\.3688\+0\.1625Global theme0\.21250\.50630\.4563\+0\.2438\-0\.0500Multi\-hop0\.15000\.34380\.4875\+0\.3375\+0\.1438Null/OOD diagnostic0\.19380\.46250\.5313\+0\.3375\+0\.0688Temporal revision0\.15000\.36880\.4875\+0\.3375\+0\.1188PSS clue retrieval’s strongest card\-relative gains occur in coreference, exact fact, multi\-hop, and entity binding\. These categories benefit from recovering a project name, component, configuration, version, or relation\-chain endpoint before retrieval\. The global\-theme card is better by five points, consistent with a structured text summary being sufficient for broad topic recovery\.

The null/OOD row in[Table27](https://arxiv.org/html/2610.33047#A14.T27)is a retrieval diagnostic, not a safety result\. A null query has no gold evidence groups, and an unguarded rewrite can still retrieve lexically related chunks\. Safety is instead measured by the router’s conditional false\-activation rate\.

Table 28:Guarded PSS action counts by category over 192 probes per category\. Counts describe behavior, not action\-specific causal quality\.CategoryRawCardPSS\-RRFActive topic705666Coreference585975Entity binding635475Exact fact785361Global theme587361Multi\-hop665967Null/OOD676461Temporal revision585480Total518472546The highest card count occurs for global theme, matching the card’s retrieval strength\. PSS\-RRF is selected most often for temporal revision and is also frequent for coreference and entity binding\. However, the router was trained to allocate actions based on observable confidence\. Comparing outcome means between selected action groups would be confounded by sample difficulty\.

## Appendix ORetriever Interaction

Table 29:All\-Recall@4 under four retrievers and five query paths\. Each LoRA value uses the same PSS clue generated by the correct state\.RetrieverRawCardPSS clueRaw \+ PSS RRFGold queryBM25 flat0\.17340\.39450\.50080\.37110\.8281Dense BGE\-small0\.08910\.05390\.23200\.21640\.5438Hierarchical summary\-leaf0\.15160\.24450\.49380\.36480\.7648Entity\-relation graph0\.15940\.32810\.47970\.35700\.8297The entity\-relation graph has the strongest gold\-query score, while BM25 has the strongest PSS\-clue score\. This inversion suggests that the graph can exploit a fully specified relation query, whereas the learned clue most reliably emits exact lexical identifiers\. The hierarchical retriever nearly matches BM25 under PSS clue retrieval and is less dependent on a single flat chunk level\.

Dense BGE\-small underperforms on every path\. The clue and benchmark contain synthetic IDs such as configuration names and checkpoints that are discriminative lexically but not necessarily close under that frozen embedding model\. The BGE\-M3 extension in[Table2](https://arxiv.org/html/2610.33047#S3.T2)reverses the strong version of this diagnosis: state All\-Recall@4 reaches 0\.3391 versus 0\.1242 for raw retrieval\. The result is encoder\-specific evidence, not a general ranking of dense retrieval or a tuned upper bound\.

Raw \+ PSS RRF is below PSS clue retrieval for all four retrievers\. Withk=4k=4, fusing weak raw\-query hits can displace one required evidence group\. This motivates the calibrated action selector rather than unconditional hybrid retrieval\.

#### Strong\-backend public confirmation\.

The second panel of[Table2](https://arxiv.org/html/2610.33047#S3.T2)uses a preregistered, task\-stratified 112\-session public subset that excludes all seven sessions used for implementation smoke testing\. Selection uses task and session IDs only; answers, target documents, and query variants are not consulted\. Each frozen backend receives the same raw, full\-history, parsed\-reference, correct\-state, matched\-wrong, shuffled\-state, RRF, and gold query sources\. This design holds the index and retriever fixed, so the paired effect measures the value of the session\-memory query interface rather than differences between document stores\.

Correct PSS clues improve All\-Recall@3 for every completed backend\. BGE\-M3, Contriever, Qwen3\-Embedding\-4B, and compatible HyDE/RQ\-RAG pipelines pass the joint Holm\-corrected rule against raw, wrong, and shuffled states\. Their individual gains over raw are 35\.71, 30\.36, 28\.57, 35\.71, and 35\.71 points, respectively\. BM25 gains 18\.75 points but its correct–wrong comparison does not survive correction; RAPTOR gains 10\.71 points but likewise fails the joint control rule\. Across all seven rows, PSS differs from the parsed reference by only−0\.89\-0\.89to\+1\.79\+1\.79points, with no significant comparison\. Thus the confirmation supports portable recovery of a structured retrieval intent through parameter states, with the parsed reference providing a text comparison whose request selection is resolved by the protocol’s explicit activity markers\.

The earlier single\-session wrong\-state reversal disappears at confirmation scale: correct PSS exceeds wrong state by 30\.36–47\.32 points for all five supported backends\. GraphRAG is reported in the cross\-model evaluation in Panel A; HippoRAG\-v2 and Cognee produced no audited scores and remain absent from the 112\-session confirmation rather than being assigned zeros\. The HyDE\-compatible and RQ\-RAG\-compatible rows isolate their query\-transformation ideas over the same BGE\-M3 backend and are labeled compatible rather than official end\-to\-end reproductions\.

## Appendix PAnswer\-Stage Diagnostics

### P\.1Reader ceilings

Table 30:Aggregate answer token F1\. Exact Match is 0 for every listed arm\.Answer pathToken F1Raw query \+ RAG0\.1570Structured card \+ RAG0\.0560Summary\-128 \+ RAG0\.0975Full\-session rewrite \+ RAG0\.0905Gold canonical query \+ RAG0\.3547Gold evidence \+ base 7B0\.2870Capped full context \+ base 7B0\.3531Gold evidence underperforming gold\-query RAG is unexpected\. Possible causes include answer/citation formatting, different evidence rendering, excessive or insufficient evidence, and reader prompt mismatch\. Because all Exact Match values are zero, retrieval\-to\-answer transition metrics based on Exact Match have no positive baseline cases\.

### P\.2Same\-query, same\-evidence state ablation

Table 31:Answer token\-F1 differences after fixing the query and retrieved chunk sequence\.ComparisonDifference95% CIH5 statusKeep correct PSS state−\-unload/base\+0\.0037\[\-0\.0040, 0\.0115\]failCorrect PSS state−\-matched wrong\+0\.0442\[0\.0369, 0\.0514\]<0\.05<0\.05Correct PSS state−\-shuffled\+0\.0042\[\-0\.0033, 0\.0121\]failTable 32:Correct\-state answer F1 gain over unloading the state, by category\.CategoryPSS gainCategoryPSS gainActive topic\-0\.0437Coreference\+0\.0427Entity binding\+0\.0250Exact fact\+0\.0249Global theme\-0\.0019Multi\-hop\+0\.0114Null/OOD\-0\.0197Temporal revision\-0\.0091No category simultaneously exceeds unloaded, wrong, and shuffled controls by 0\.05\. Correct\-versus\-wrong is positive because the wrong adapter can corrupt the decoder, but correct\-versus\-unloaded and correct\-versus\-shuffled are near zero\. The state is therefore not a reliable decoder\-side memory\.

### P\.3Vacuous transition statistic

The generated report containsresilience\_rate=1\.0; however,resilience=0and there are zero Exact\-Match\-correct baseline cases\. The value results from the implementation’s empty\-denominator convention, so we exclude it from evidence of success\. All 1,536 probe pairs are in the “no recovery” cell under Exact Match\.

### P\.4Reader\-analysis improvements

Before using answer results to assess the broader architecture, a future run could strengthen the analysis by:

1. 1\.separate answer text from citations before normalization;
2. 2\.support multiple reference answers and standard token\-F1;
3. 3\.report answerable and null probes separately;
4. 4\.inspect gold\-evidence rendering and order;
5. 5\.use a prompt that requests the same output schema as the references;
6. 6\.manually audit a stratified answer sample;
7. 7\.retain the same\-query, same\-evidence ablation after repair\.

## Appendix QSemantic\-Peak Capacity Diagnostic

The semantic\-peak experiment asks where a fixed state ceases to retain at least 90% of its low\-load retrieval behavior\. It crosses eight semantic categories, five ranks, and six independent load axes:

\|H\|∈\{1​K,4​K,16​K,65​K\},topics∈\{1,2,4,8\},same\-type entities∈\{2,4,8,16\},hops∈\{1,2,3,4\},revisions∈\{0,1,2,4\},evidence sections∈\{1,2,4,8\}\.\\begin\{split\}&\|H\|\\in\\\{1\\mathrm\{K\},4\\mathrm\{K\},16\\mathrm\{K\},65\\mathrm\{K\}\\\},\\\\ &\\text\{topics\}\\in\\\{1,2,4,8\\\},\\quad\\text\{same\-type entities\}\\in\\\{2,4,8,16\\\},\\\\ &\\text\{hops\}\\in\\\{1,2,3,4\\\},\\quad\\text\{revisions\}\\in\\\{0,1,2,4\\\},\\\\ &\\text\{evidence sections\}\\in\\\{1,2,4,8\\\}\.\\end\{split\}The balanced constrained design yields 240 category–rank–axis combinations\. Only 42 combinations \(17\.5%\) have an identifiable breakpoint\. The remainder are flat, noisy, or never cross the registered 90% threshold within the observed levels\.

This result is insufficient to fit a stable capacity law\. In particular, it does not show that increasing rank monotonically shifts every breakpoint or that rank 32 is saturated\. The diagnostic is retained because it prevents a misleading single aggregate from being presented as evidence of unbounded retention\. A future capacity study needs more sessions per cell, multiple writer seeds, and a monotone model specified before observing outcomes\.

## Appendix RRQ4: Inference, Storage, and Break\-Even Accounting

We distinguish the original 16\-token profile below from the complete 64\-token clue/retrieval/router profile in[SectionV\.5](https://arxiv.org/html/2610.33047#A22.SS5)\. The latter includes both LLM calls, all three retrieval calls, and card input for Guarded PSS, and supplies the eight\-session workload block in[Figure4](https://arxiv.org/html/2610.33047#S3.F4)\(b\)\. The two profiles retain their own measured write times and amortization estimates\.

Relative to the available mixed\-length full\-history profile, the Qwen PSS clue path uses 98\.97% fewer online prompt tokens, 67\.64% lower total latency, and 11\.60% lower peak allocation\. Its 29\.03\-second offline write amortizes after an estimated 43 repeated reads against average full\-history prefill, but never against the 32\-token card\. Audited logical states occupy 44, 40, and 24 MiB per session for Qwen, Mistral, and Phi, respectively\. These measurements describe the tested hardware and workload rather than a universal efficiency law\.

### R\.1Online profile

Table 33:Measured online profile on 16 sessions with 16 generated tokens\. “Swap/setup” is the measured adapter or state\-transition overhead recorded by the harness\.MethodPromptGenerationSwap/setupPeak alloc\.Full\-history prefill5522\.001\.0144 s–17\.368 GBPSS clue path56\.750\.3054 s0\.0228 s15\.353 GBStructured card\-3280\.750\.3079 s0\.0155 s15\.362 GBRecent\-12896\.750\.3329 s0\.0171 s15\.368 GBThe average full\-history row mixes available 1K, 4K, and 16K profiles\. Configured 65K and 128K rows are unavailable because they exceed the model input cap or source length\. The reported state total of 0\.3282 seconds is generation plus swap\. The 56\.75 prompt tokens include the current query, instruction, and output template, so the online request is not token\-free\.

### R\.2State bytes and residency

Table 34:State construction and multi\-session residency\.QuantityValueOffline write time per session29\.033 sLogical state bytes46,137,344Physical state bytes46,175,478 \(44\.04 MiB\)Physical bytes for 256 test states11,820,922,368 \(11\.01 GiB\)Estimated states at 80% free\-GPU budget579Four\-state LRU hit rate0\.8125Mean host\-to\-device latency on miss0\.01658 sMean adapter swap latency in LRU profile0\.00205 sThe early rank\-8 pilot used roughly 11 MiB per state, but the final rank\-32 method uses 44\.04 MiB\. Only the latter is relevant to the main result\. The 579\-state estimate is a capacity calculation under the observed free\-memory snapshot, not a sustained serving benchmark\.

### R\.3Amortization

For methodmmandNNreads, the accounting is

Cm​\(N\)=Cmwrite\+N⁡\(Cmretrieve\+Cmread\)\.C\_\{m\}\(N\)=C^\{\\mathrm\{write\}\}\_\{m\}\+N\(C^\{\\mathrm\{retrieve\}\}\_\{m\}\+C^\{\\mathrm\{read\}\}\_\{m\}\)\.\(6\)Under the measured latency components, LoRA crosses average full\-history prefill at 43 reads\. It never crosses the text\-card path because the card has no model\-optimization write and similar online generation cost\. Storage, index construction, and task value are not collapsed into this latency\-only break\-even; we report them separately\.

The parsed sealed\-test active request averages only 65\.65 UTF\-8 bytes\. The logical Qwen, Mistral, and Phi states are therefore approximately702,831×702\{,\}831\\times,638,937×638\{,\}937\\times, and383,362×383\{,\}362\\timeslarger than that raw text, excluding container overhead\. On the public extension, PSS\-minus\-reference differences are negative for both retrieval \(−0\.38/−2\.29/−1\.53\-0\.38/\-2\.29/\-1\.53points\) and answer F1 \(−1\.77/−1\.49/−3\.96\-1\.77/\-1\.49/\-3\.96\) for Qwen/Mistral/Phi\. The public parsed\-reference and compact\-card settings therefore represent different information budgets\. The PSS\-320 compact\-card comparison measures session\-scope recovery, while[SectionV\.4](https://arxiv.org/html/2610.33047#A22.SS4)separately isolates the value of retrieved evidence for a fixed reader question\.

### R\.4What is and is not bounded

For one active session, online historical state is bounded by one fixed adapter plus fixed retrieval/query/generation budgets\. Offline write activations are bounded by the 128\-token chunk, but write steps grow with history length\. Across sessions, adapter storage is linear\. During generation, KV still grows with the current prompt and output\. These distinctions prevent the efficiency profile from being described as strict constant total memory\.

## Appendix SStatistical Analysis Details

### S\.1Unit of analysis

Each session contributes six correlated probes\. Probe rows are first aggregated within session; they are not treated as 1,536 independent observations\. Bootstrap resampling is paired across methods and stratified by the eight semantic categories\. The final intervals use 10,000 resamples and a fixed experiment seed\.

### S\.2Binary paired tests

For H1, 134 of 256 sessions are correct only under the guarded state method, zero are correct only under raw retrieval, and 134 are discordant\. The exact McNemarpp\-value is9\.18×10−419\.18\\times 10^\{\-41\}and the Holm\-adjusted value is1\.84×10−401\.84\\times 10^\{\-40\}\.

For H2, 56 sessions are correct only under guarded state retrieval and seven only under the card, yielding 63 discordant pairs\. The exact and Holm\-adjustedpp\-value is1\.36×10−101\.36\\times 10^\{\-10\}\. H2 is a non\-inferiority question, so its primary decision uses the paired difference interval\[0\.0898,0\.1344\]\[0\.0898,0\.1344\]relative to the−0\.02\-0\.02margin\. The smallpp\-value is supporting paired binary evidence, not the non\-inferiority test itself\.

### S\.3Bootstrap results

Table 35:Session\-clustered paired bootstrap intervals\.ComparisonnnsessionsDifference95% CIGuarded−\-raw All\-Recall@4256\+0\.3328\[0\.3063, 0\.3586\]Guarded−\-card All\-Recall@4256\+0\.1117\[0\.0898, 0\.1344\]Full history−\-query\-only32\+0\.1188\[0\.0375, 0\.2188\]Keep correct−\-unload F1256\+0\.0037\[\-0\.0040, 0\.0115\]Correct−\-shuffled F1256\+0\.0042\[\-0\.0033, 0\.0121\]Correct−\-wrong F1256\+0\.0442\[0\.0369, 0\.0514\]
### S\.4Multiplicity and exploratory analyses

H1 and H2 form the corrected primary family\. Category, retriever, semantic peak, efficiency, and answer\-category analyses are exploratory and are interpreted through effect sizes rather than uncorrected significance claims\. H3 uses registered 0\.10 causal\-gap thresholds; the current summary does not include bootstrap intervals for each retrieval control gap, which is a reporting item for a future comprehensive report\. The public extension uses one six\-comparison Holm family \([Table16](https://arxiv.org/html/2610.33047#A7.T16)\); its dagger marks guarded candidates that beat raw, parsed reference, and full\-history rewriting, and no public row meets this rule\. The PSS\-320 BGE\-M3/GraphRAG extension uses one four\-comparison Holm family and assigns daggers only to the two state rows that beat both raw and card\.

### S\.5Failures and denominators

All stage audits report zero issues and the maximum arm failure rate is zero\. The main artifact contains 43,008 rows across arms and controls\. A camera\-ready result table would benefit from per\-metric and per\-arm counts for total, valid, missing, empty\-output, OOM, NaN, and timeout cases; aggregate stage success alone does not prove identical denominators for every auxiliary metric\. The public aggregate contains 4,192 rows with complete 262\-session coverage, and its write audit reports 652/652 states and zero failures\.

## Appendix TReproducibility Checklist

### T\.1Completed artifacts

PSS\-320 source JSONL, generator, manifest, and automated audit; source\-group\-disjoint calibration/test split and sealed\-test hash; deterministic 32/16/16 calibration subsplits; formal\-answer exclusion contract for writer training; correct, matched\-wrong, shuffled, and zero\-reset controls; writer objective, rank, topology, history, content, and precision configurations; four retriever implementations and the three\-way router; pinned LongBench/InfiniteBench adapters, public sessionization, deterministic 32/32/262 split, and null/OOD controls; BGE\-M3 and GraphRAG PSS\-320 runs; frozen Qwen/Mistral/Phi\-3 portability contracts with architecture\- native LoRA targets and audited 44/40/24 MiB logical states; pinned original and sessionized UltraDomain tracks, with exact\-document\-hash grouping and explicit PSS non\-applicability on the original QA task; 652\-state write manifest with zero failures and complete three\-shard coverage; session\-clustered bootstrap and exact McNemar implementation; session\-level sign\-flip tests with Holm correction and generated best/second\-best/dagger formatting; a preregistered, independently generated PSS\-Carrier\-320 confirmation with 320 sessions and three writer seeds, using target\-only, history\-only, matched persistent\-text, wrong\-state, and shuffled\-state controls under BGE\-M3 and BM25; stage, environment, checksum, and run auditors, with no formal blocker in the cross\-model run; unit and smoke tests covering adapters, leakage, merge, statistics, formatting, resume behavior, and model\-specific chat templates\.

### T\.2Key run configuration

Table 36:Configuration used to reproduce the reported state\.FieldValuePrimary backboneQwen2\.5\-7B\-InstructPortability backbonesMistral\-7B\-Instruct\-v0\.2; Phi\-3\-mini\-128kPrecisionBF16Writer objectiveretrieval\_alignedPrimary PSS\-320 writer seeds91, 92, 93Carrier\-confirmation writer seeds91, 92, 93Carrier\-confirmation cohortPSS\-Carrier\-320; 320 independent sessionsLoRA rank / alpha32 / 64LoRA layersfinal 8Topologysingle slotHistory coveragefull ordered historyLM chunk / minimum steps128 / 16LM / readout learning rate2×10−52\{\\times\}10^\{\-5\}/10−410^\{\-4\}Readout / retrieval steps32 / 32Retrieval margin0\.2RAG chunk / overlap / top\-kk192 / 48 / 4Public RAG chunk / overlap / top\-kk512 / 64 / 3Public split seed / counts20260812 / 32, 32, 262Public dense retrieverBGE\-M3, pinned revisionPortability split/test seedsession\-disjoint / 20260812UltraDomain released countsFin 345; Legal 438; Mix 130UltraDomain sessionized sealed test112 sessionsRRF constant60Rewrite / answer budget64 / 64 new tokensFull\-context input cap32,768 tokens
### T\.3Hardware and scheduling

The seed\-specific runs were distributed across separate machines\. The primary Qwen aggregation used H200 hardware; the state\-fingerprint and functional\-alignment diagnostics, public extension, and cross\-model runs used three GPUs reported by their runtime as NVIDIA GeForce RTX 4090 with 49,140 MiB each\. Every reported state\-writing analysis aggregates writer seeds 91–93\. Calibration and write stages scheduled up to two short\-sequence processes per GPU; full main generation scheduled one process per GPU\. Capacity checks required 23,000 MiB per calibration/write job and 32,000 MiB per main job\. Completed markers allowed interruption\-safe resume\. The public extension used one process on each GPU for state writing and each evaluation split\. The cross\-model run used the same three devices; its audit verified pinned safetensors for Mistral, Phi\-3, and BGE\-M3, dataset checksums, architecture\-native target coverage, sufficient disk, and zero formal blockers\. The audited environment reports PyTorch 2\.5\.1\+cu124, Transformers 4\.57\.6, Datasets 5\.0\.1, Sentence\-Transformers 3\.4\.1,rouge1\.0\.1, androuge\-score0\.1\.2\.

### T\.4Frozen RQ2 state\-geometry run

The RQ2 script reads the already\-audited states and does not train or alter a model\. Writer outputs are aggregated over seeds 91–93; the separate preregistered analysis seed is 20260814, with eight Rademacher projections per LoRA pair, 10,000 label permutations, 15 UMAP neighbors, cosine distance, and minimum distance 0\.1\. On the server, after installingumap\-learn==0\.5\.7from the configured package mirror\. The command refuses to overwrite an existing output directory, embedding/energy CSV files, PDF/PNG figures, and a LaTeX fragment whose numbers are generated from the JSON result\. The fragment enters the paper workspace after the cross\-machine audit confirms all 768 state instances \(256 held\-out sessions for each of writer seeds 91–93\), complete category coverage, and non\-empty figures\.

## Appendix UQualitative and Error\-Analysis Protocol

The registered protocol specifies a stratified, double\-annotated sample of 100 failed sessions with adjudication\. Planned labels cover:

- •session scope, project identification, or entity/configuration binding;
- •temporal revision or superseded\-version conflict;
- •incomplete multi\-hop evidence or retriever miss despite a usable rewrite;
- •router misroute, evidence neglect, or unsupported/invalid generation\.

Planned materials include the complete session, raw/card/state rewrites and rankings, router scores, gold evidence groups, and answer outputs\. Reporting includes raw agreement, Cohen’sκ\\kappa, and third\-annotator adjudication\.

No completed manual error labels are present, so we report neither fabricated counts nor selected traces\. Quantitative patterns motivate three audit hypotheses: cards may favor broad themes; LoRA may help when identifiers are missing; and reader failures may persist after correct retrieval\. These remain unvalidated qualitative hypotheses\.

This failure\-taxonomy exercise is separate from the completed 32\-session human audit of PSS\-320 construction and label quality described in[AppendixI](https://arxiv.org/html/2610.33047#A9)\.

The four planned case quadrants are: LoRA correct/card wrong, card correct/LoRA wrong, both correct, and both wrong\. Published examples would include retrieved chunk IDs and exact source spans to support verification of the claimed mechanism\.

## Appendix VSession\-State Readout and Complete Serving Costs

PSS compiles session information into a reusable parameter state from which retrieval text can be generated online or materialized for subsequent reuse\. This appendix studies that compilation\-and\-readout path through information\-matched text controls, readout interfaces, and complete online cost accounting\. Protocols S and R analyze 32 existing sessions, three writer seeds \(91–93\), and a shared 256\-session candidate corpus\. A separate question\-conditioned extension evaluates distinct historical\-record banks on sixteen composite memory groups \([SectionV\.3](https://arxiv.org/html/2610.33047#A22.SS3)\)\. These experiments complement the original benchmark and the independent carrier confirmation\.

### V\.1Information\-matched text controls

#### Text\-state roles\.

A compact structured card, a parsed active\-request reference, and a supplied retrieval clue represent different text states\. The original PSS\-320 compact\-card comparison tests recovery of session scope under a short online context: PSS clue retrieval reaches 50\.08% versus 39\.45% for the card, a 10\.63\-point gain\. Guarded PSS reaches 50\.63%, an 11\.18\-point gain over that card\.

In the public sessionization protocol, the parsed active\-request reference preserves the complete request designated by the history’s explicit activity marker\. This request is the protocol\-defined target for active\-request reconstruction and also supplies the positive readout target during session\-specific PSS writing\. Direct retrieval with this resolved request provides a reference for evaluating how much of its retrieval utility PSS recovers through parameter readout\. This reference characterizes retrieval when request selection is already determined\.

#### Protocol S: text\-memory controls\.

The compiler and generated\-text baselines receive the same ordered history and answer\-free positive/negative clues\. Text memories are generated independently at 128\-, 256\-, and 512\-token budgets; a separate 256\-token structured format records current identifiers, relations, and superseded alternatives\. Each short budget is generated directly rather than extracted as a prefix of a longer memory\. Direct caches retain the supplied positive clue, the current query plus that clue, or a labeled positive/negative pair\. The fixed session selection yields 4,800 retrieval rows across BGE\-M3 and BM25\. Formal answers and gold rewrites are excluded from memory construction\.

Table 37:Session\-level evidence All\-Recall@4 \(percent\), with complete method coverage in each protocol\. S and R reuse the same 32 sessions and 96 states but execute separate readout runs; their estimates are reported separately\. A dash denotes a method outside that protocol, not a zero score\.Text\-memory controls \(S\)Readout controls \(R\)MethodBGE\-M3BM25BGE\-M3BM25Raw query11\.8816\.2511\.8816\.25Supplied clue61\.2585\.0061\.2585\.00Query \+ supplied clue60\.6287\.5060\.6287\.50Query \+ labeled clue pair57\.5086\.88––Compact card\-32 rewrite6\.8838\.75––Text\-128 rewrite17\.5047\.50––Text\-256 rewrite15\.0043\.7515\.0043\.12Text\-512 rewrite20\.0046\.8820\.6248\.12Structured\-256 rewrite16\.8848\.1217\.5047\.50Base\-model rewrite––2\.5013\.75Supplied clue\-pair rewrite––15\.0046\.25PSS online readout23\.9642\.9223\.5442\.71Matched\-wrong PSS0\.212\.080\.212\.08Query \+ fixed PSS readout––64\.3880\.83Fixed PSS readout \+ base rewrite––7\.9230\.00
#### Shared\-state readout protocol\.

Protocol R reuses the same 96 serialized PSS states and selected sessions; it adds readout controls without another training stage\. Each state is read once with the fixed training instruction, “Return only a compact search clue for the active session\.” This produces a query\-independent textcsc\_\{s\}before any future probe is supplied\. The two protocols execute separate generation passes; Table[37](https://arxiv.org/html/2610.33047#A22.T37)preserves both sets of estimates\. The analysis is a targeted follow\-up on previously evaluated sessions, distinct from the independently generated PSS\-Carrier\-320 cohort\.

### V\.2Online parameter readout and PSS\-derived text reuse

Protocol R evaluates two reuse interfaces originating from the same compiled stateΔs\\Delta\_\{s\}\. Online parameter readout generatesGθ\+Δs​\(q\)G\_\{\\theta\+\\Delta\_\{s\}\}\(q\)for each request\. Fixed readout first producescs=Gθ\+Δs​\(c0\)c\_\{s\}=G\_\{\\theta\+\\Delta\_\{s\}\}\(c\_\{0\}\)from the training instructionc0c\_\{0\}, before any future probe is supplied, and then reusescsc\_\{s\}as a text cache\. The text interfaces include direct retrieval fromq\+csq\+c\_\{s\}and base\-model rewriting from\(q,cs\)\(q,c\_\{s\}\), alongside supplied\-clue caches\. Base\-only and matched\-wrong controls test parameter conditioning and session correspondence\. Text\-256, Text\-512, and Structured\-256 remain additional text\-memory controls\. The protocol contains 3,200 query rows and 6,400 retrieval rows; each PSS\-derived cache retains the seed of its source state\.

#### State\-conditioned rewriting\.

Relative to the base\-only rewrite, online PSS improves BGE\-M3 and BM25 All\-Recall@4 by 21\.04 and 28\.96 points, respectively, with positive Holm\-corrected effects\. On BGE\-M3, it also improves over rewriting from the fixed PSS text readout by 15\.62 points \(pH=0\.00035p\_\{H\}=0\.00035\)\. These comparisons identify a useful parameter\-conditioning mechanism within the tested rewriting interface\. The corresponding BM25 effect over cached\-readout rewriting is 12\.71 points \(pH=0\.0826p\_\{H\}=0\.0826\)\.

#### Materializing a PSS\-derived retrieval cache\.

The fixed\-readout path reaches 64\.38% All\-Recall@4 on BGE\-M3 and 80\.83% on BM25 usingq\+csq\+c\_\{s\}\. The corresponding supplied\-clue cacheq\+zs\+q\+z\_\{s\}^\{\+\}reaches 60\.62% and 87\.50%\. Herecsc\_\{s\}is generated from the optimized session state rather than copied directly from the supplied clue\. These results show that a compiled parameter state can produce useful retrieval text for subsequent reuse\. Online parameter readout and materialized text reuse are two operational interfaces to this compilation path: one conditions each request onΔs\\Delta\_\{s\}, and the other persists its fixed readoutcsc\_\{s\}\.

The reported retrieval scores characterize the complete interfaces\. Fixed readout usesq\+csq\+c\_\{s\}, whereas the online PSS arm retrieves with its generated string without an additional raw\-query concatenation\. Table[39](https://arxiv.org/html/2610.33047#A22.T39)reports the paired rewrite comparisons; the fixed\-cache versus supplied\-cache means above are descriptive\. A materialized PSS cache incurs the original state compilation and one fixed readout before text\-only serving\.

#### Statistical unit and generation budget\.

We average probes within a seed and seeds within a session, then perform two\-sided paired session\-level sign\-flip tests with bootstrap intervals\. Protocol S has 10 primary and four secondary comparisons; R has 12 primary and 10 secondary comparisons\. Holm correction is applied separately to each complete family across both retrievers\. The intervals in the tables are unadjusted intervals, and a positive interval endpoint pattern does not replace the corrected test\. All selected answerable probes and all methods are retained; descriptive category/probe strata do not define additional confirmatory claims\.

Online generation uses the same greedy raw\-prompt protocol and 64\-token cap in every generated arm\. S’s generated memories and online rewrites all use their full generation budgets\. Its estimates therefore characterize this fixed\-budget interface; short natural termination is not assumed\. R keeps that decoding policy and reuses S’s independently generated text memories\. Finite\-logit checks retain finite empty responses, and empty retrieval strings retrieve no evidence\.

Table 38:Protocol S: PSS online readout minus each reference \(percentage points\)\. Two\-sided paired tests use session means;pHp\_\{H\}is Holm\-adjusted within each listed family across both retrievers\. Intervals are unadjusted paired bootstrap intervals\. Missing S\-secondary intervals were not included in the source summary\.ReferenceBGE\-M3BM25Δ\\Delta95% CIpHp\_\{H\}Δ\\Delta95% CIpHp\_\{H\}Primary familySupplied clue\-37\.29\[\-49\.38, \-25\.00\]<0\.001<0\.001\-42\.08\[\-53\.12, \-31\.25\]<0\.001<0\.001Query \+ supplied clue\-36\.67\[\-50\.00, \-23\.96\]<0\.001<0\.001\-44\.58\[\-55\.00, \-34\.17\]<0\.001<0\.001Text\-256 rewrite\+8\.96\[\+1\.25, \+17\.08\]0\.240\-0\.83\[\-11\.88, \+10\.42\]1\.000Text\-512 rewrite\+3\.96\[\-6\.67, \+14\.79\]1\.000\-3\.96\[\-15\.62, \+7\.92\]1\.000Structured\-256 rewrite\+7\.08\[\-0\.63, \+14\.79\]0\.514\-5\.21\[\-19\.38, \+8\.33\]1\.000Secondary familyRaw query\+12\.08–0\.004\+26\.67–<0\.001<0\.001Matched\-wrong PSS\+23\.75–<0\.001<0\.001\+40\.83–<0\.001<0\.001Table 39:Protocol R: PSS online readout minus each reference \(percentage points\)\. Two\-sided paired tests use session means;pHp\_\{H\}is Holm\-adjusted within each listed family across both retrievers\. Intervals are unadjusted paired bootstrap intervals\.ReferenceBGE\-M3BM25Δ\\Delta95% CIpHp\_\{H\}Δ\\Delta95% CIpHp\_\{H\}Primary familySupplied clue\-37\.71\[\-50\.21, \-25\.42\]<0\.001<0\.001\-42\.29\[\-53\.12, \-31\.46\]<0\.001<0\.001Query \+ supplied clue\-37\.08\[\-50\.62, \-24\.38\]<0\.001<0\.001\-44\.79\[\-55\.62, \-33\.75\]<0\.001<0\.001Base\-model rewrite\+21\.04\[\+12\.92, \+29\.38\]<0\.001<0\.001\+28\.96\[\+19\.38, \+38\.54\]<0\.001<0\.001Supplied clue\-pair rewrite\+8\.54\[\-0\.83, \+18\.12\]0\.194\-3\.54\[\-16\.46, \+9\.17\]0\.623Query \+ fixed PSS readout\-40\.83\[\-53\.54, \-28\.33\]<0\.001<0\.001\-38\.12\[\-49\.58, \-26\.88\]<0\.001<0\.001Fixed PSS readout \+ base rewrite\+15\.62\[\+8\.96, \+22\.71\]<0\.001<0\.001\+12\.71\[\+2\.29, \+22\.92\]0\.083Secondary familyRaw query\+11\.67\[\+4\.38, \+18\.96\]0\.038\+26\.46\[\+17\.29, \+35\.83\]<0\.001<0\.001Text\-256 rewrite\+8\.54\[\+1\.04, \+16\.67\]0\.297\-0\.42\[\-11\.25, \+10\.42\]1\.000Text\-512 rewrite\+2\.92\[\-7\.71, \+13\.75\]1\.000\-5\.42\[\-16\.88, \+6\.46\]1\.000Structured\-256 rewrite\+6\.04\[\-1\.67, \+13\.96\]0\.811\-4\.79\[\-19\.17, \+8\.75\]1\.000Matched\-wrong PSS\+23\.33\[\+16\.04, \+30\.83\]<0\.001<0\.001\+40\.62\[\+31\.67, \+49\.79\]<0\.001<0\.001

### V\.3Question\-conditioned readout from distinct historical records

PSS supports selective access to multiple historical records through one compiled parameter state\. Given an incoming question, the state generates retrieval text without supplying the persistent text bank to the readout model\. We evaluate this capability with distinct\-record memory banks, using mechanism controls to assess state\-dependent access and text selectors to compare alternative access interfaces\.

#### Protocol and information boundary\.

We construct eight development and sixteen evaluation memory groups from 96 source sessions, with four sessions per group and no overlap across groups or splits\. Each source contributes an action, a configuration, a rationale, and a complete relation path\. TheK=4K=4bank contains one record from each source, covering the four record types;K=16K=16adds the remaining twelve records\. Each evaluation group has five alias\-conditioned questions, including a second expression for an action record\. Both bank sizes use the same 80 questions and the complete 256\-session test corpus; development uses the 64\-session calibration corpus\. Evidence targets are the historical record spans relevant to each question\.

Parameter and text methods receive the same historical records and alias associations\. The records contain factual content, potentially including answers, making this an extension distinct from the primary answer\-free protocols\. Bank construction excludes evaluation questions, answers, and gold rewrites\. Training instructions and evaluation expressions are separate; evaluation questions retain explicit aliases and record\-type cues\.

#### Question\-conditioned compilation\.

A bank\-only writer trains on four question–record templates per record, using the positive/negative sequence objective without a preceding history\-LM phase\. Four visits per training pair yield 64 updates forK=4K=4and 256 forK=16K=16, holding per\-record exposure constant\. Writer seed 91 produces 16 development and 32 evaluation states\. Local PSS and base\-model generation use the native chat instruction, greedy decoding, EOS handling, and a 256\-token output cap\. Generated or selected text is concatenated with the original question before evidence retrieval\.

#### Access interfaces\.

All\-record concatenation forms one query from the entire bank; record\-wise RRF retrieves separately for each record and fuses the rankings\. BM25 and BGE selectors choose one or two records from the text bank\. Grok\-based record selection makes one API call per question to select a record from the complete bank and its metadata\. LLM bank rewriting uses the base model to generate a retrieval expression from the question and the bank\. PSS accesses the compiled parameter state without bank\-text input\. Wrong\-group PSS uses another group’s state with the same alias vocabulary\. The separately reported target\-record reference uses the evaluator’s target record ID and is excluded from text\-policy selection\.

Table 40:Mechanism controls for question\-conditioned parameter readout: group\-averaged evidence All\-Recall@4 \(percent\)\. Both bank sizes use the same 16 evaluation groups and 80 questions\. Text\-selection and rewriting comparisons are reported in Table[41](https://arxiv.org/html/2610.33047#A22.T41)\.K=4K=4K=16K=16MethodBGE\-M3↑\\uparrowBM25↑\\uparrowBGE\-M3↑\\uparrowBM25↑\\uparrowRaw query0\.000\.000\.000\.00Base\-model rewriting0\.001\.250\.001\.25All\-record concatenation25\.0047\.5018\.7535\.00Record\-wise RRF53\.7557\.5016\.2540\.00PSS parameter readout76\.2583\.7583\.7595\.00Wrong\-group PSS1\.250\.001\.250\.00
#### Selective access through parameter state\.

AtK=16K=16, PSS reaches 83\.75% All\-Recall@4 with BGE\-M3 and 95\.00% with BM25\. Compared with all\-record concatenation, the gains are 65\.00 and 60\.00 percentage points\. Compared with record\-wise RRF, PSS gains 67\.50 and 55\.00 points while reducing the number of evidence queries from sixteen to one\. Wrong\-group PSS reaches 1\.25% and 0\.00%, supporting the role of group\-specific information in parameter readout\. AtK=4K=4, PSS reaches 76\.25% and 83\.75%, exceeding concatenation by 51\.25 and 36\.25 points\. The two bank sizes jointly vary memory content and total write updates while keeping exposure per record constant\.

Table 41:Text\-selection and rewriting interfaces under the same distinct\-record protocol\. Values are group\-averaged evidence All\-Recall@4 \(percent\); the PSS row is repeated for comparison\. The target\-record reference uses evaluation information and is excluded from text\-policy selection\. Selector top\-1/top\-2 denotes the number of memory records included in the query; the final evidence cutoff is four throughout\. Table[42](https://arxiv.org/html/2610.33047#A22.T42)reports descriptive differences from development\-selected strategies\.K=4K=4K=16K=16MethodBGE\-M3↑\\uparrowBM25↑\\uparrowBGE\-M3↑\\uparrowBM25↑\\uparrowBM25 selector, top\-172\.5097\.5077\.5088\.75BM25 selector, top\-267\.5095\.0071\.2591\.25BGE selector, top\-172\.5097\.5070\.0091\.25BGE selector, top\-270\.0090\.0068\.7592\.50Grok\-based record selection77\.5097\.5077\.5097\.50LLM bank rewriting56\.2583\.7556\.2592\.50PSS parameter readout76\.2583\.7583\.7595\.00Target\-record reference77\.5097\.5083\.7597\.50
#### Comparison with text access\.

AtK=16K=16, PSS achieves the highest BGE\-M3 mean among the evaluated non\-reference methods, exceeding the strongest reported text score of 77\.50% by 6\.25 points\. With BM25, PSS reaches 95\.00%, exceeding all four retrieval\-based selector configurations and bank rewriting; Grok selection reaches 97\.50%\. These results demonstrate question\-conditioned retrieval through parameter state across both backends, with a BGE\-M3 advantage in the sixteen\-record setting\. Table[42](https://arxiv.org/html/2610.33047#A22.T42)summarizes descriptive mean differences from the development\-selected text strategies\.

Table 42:Descriptive PSS\-minus\-text differences against the strategy selected on development for each bank size and retriever\. Values are differences in group\-averaged All\-Recall@4, in percentage points, over the same 16 evaluation groups\.KKRetrieverDevelopment\-selected text strategyDifference \(pp\)4BGE\-M3BM25 selector, top\-1\+3\.75\+3\.754BM25BM25 selector, top\-1−13\.75\-13\.7516BGE\-M3Grok\-based record selection\+6\.25\+6\.2516BM25LLM bank rewriting\+2\.50\+2\.50
#### Online access workload\.

PSS uses one parameter\-conditioned generation and one evidence query per question, without supplying memory text to the LLM\. Grok selection uses one external model call followed by one evidence query; bank rewriting also uses one generation and one evidence query\. Concatenation uses one evidence query, whereas record\-wise RRF usesKK\. This comparison separates model\-based memory access from evidence\-retrieval branching\.

The archived local component profile reports mean bank\-rewriting memory inputs of 485\.06 and 1367\.69 tokens atK=4K=4andK=16K=16, respectively\. AtK=16K=16, mean generated lengths are 63\.60 tokens for PSS and 16\.89 for bank rewriting\. In[Figure4](https://arxiv.org/html/2610.33047#S3.F4)\(b\), NR denotes unreported Grok memory\-input token usage\. Call counts, input length, output length, and state loading are separate workload dimensions; the serving\-cost profile is reported in[SectionV\.5](https://arxiv.org/html/2610.33047#A22.SS5)\.

### V\.4Evidence\-controlled answering

The answer\-stage analysis uses a fixed 16\-session subset of S\. For the controlled interface, every method answers the same explicit gold rewrite with the same frozen, unloaded reader; only the retrieved evidence changes\. PSS evidence improves F1 over raw\-query evidence by 6\.03 points \(95% CI\[2\.64,9\.23\]\[2\.64,9\.23\],pH=0\.0214p\_\{H\}=0\.0214\), with seed\-specific gains of 4\.53, 7\.87, and 5\.69 points\. This isolates a contribution of evidence access to answering under a common question\. The explicit question is an evaluation control and is never provided to the memory writer or retriever\.

A second interface uses each method’s retrieval string as the reader’s question\. Table[43](https://arxiv.org/html/2610.33047#A22.T43)reports both interfaces under one eight\-comparison Holm family\. For this second interface, PSS\-minus\-raw is−6\.89\-6\.89F1 points\. Together, the two interfaces distinguish an evidence benefit from preservation of the user’s answer request: a retrieval clue and a reader question perform different roles\. The public 1\.03% to 20\.00% F1 comparison describes its full query\-and\-evidence interface; the controlled result here establishes evidence attribution on its own 16\-session evaluation scope\.

Table 43:Answer\-interface analysis on 16 sessions from S\. Effects are PSS minus reference; Holm correction covers all eight comparisons\. Both interfaces use the same retrieved evidence for a given method and probe\.Reader inputReferenceΔ\\DeltaF1 \(pp\)95% CI \(pp\)pHp\_\{H\}Fixed questionRaw query\+6\.03\[\+2\.64, \+9\.23\]0\.021Fixed questionQuery \+ supplied clue\-6\.95\[\-14\.27, \+0\.24\]0\.252Fixed questionText\-256 rewrite\+2\.40\[\-3\.16, \+7\.53\]0\.803Fixed questionStructured\-256 rewrite\+1\.18\[\-2\.67, \+4\.68\]0\.803Retrieval query as questionRaw query\-6\.89\[\-9\.49, \-4\.48\]<0\.001<0\.001Retrieval query as questionQuery \+ supplied clue\-7\.92\[\-10\.98, \-4\.90\]0\.002Retrieval query as questionText\-256 rewrite\-5\.28\[\-8\.84, \-2\.15\]0\.021Retrieval query as questionStructured\-256 rewrite\-3\.49\[\-6\.79, \-0\.43\]0\.214Table 44:Complete online clue/retrieval/router costs for S: eight sessions, three writer seeds, three timed repeats \(72 requests per method\), BM25, and a 64\-token readout budget\. Prompt and Hist\. count total and history\-derived tokens in LLM prompts; a directly searched cached clue is not an LLM input\. LM/Ret\. count model and retrieval calls\. Final answering and offline indexing are excluded\.MethodMean \(s\)p50 \(s\)p95 \(s\)PromptHist\.LMRet\.Raw query0\.00350\.00340\.00400\.000\.0001Query \+ supplied clue0\.00510\.00510\.00550\.000\.0001Compact card rewrite1\.28431\.28301\.291381\.3821\.6211PSS clue1\.34151\.34011\.349256\.750\.0011Full\-history rewrite2\.61861\.82305\.34498495\.008435\.2511Complete Guarded PSS2\.62962\.62912\.6420138\.1221\.6223Figure 10:History\-derived tokens supplied to LLM prompts in the complete cost profile\. Brackets give LLM/retrieval call counts\. The pseudo\-log axis includes a true zero\. Direct clue retrieval uses persistent text as a retrieval query without an LLM prompt; its zero plotted value does not denote an absent text cache\.
### V\.5Complete online accounting

The cost profile measures eight sessions, three seeds, and three timed repeats \(72 requests per method\) on the reported RTX 4090 with a reported 47\.37 GiB device capacity\. It uses BM25, warm indexes, CPU\-resident states, and 64\-token readout generation\. Timings include the complete clue/retrieval/router path and state unloading; common final answering, offline model/index construction, and disk state\-cache misses are outside this online boundary\.

Pure PSS requires one clue generation and one retrieval, with no history\-derived text in its LLM prompt\. It takes 1\.341 seconds on average versus 2\.619 seconds for full\-history rewriting, a 48\.8% reduction under this workload\. Complete Guarded PSS executes two generations and three retrievals, including the card branch, and takes 2\.630 seconds\. It reads 21\.625 card tokens in its LLM prompts; its total prompt count is 138\.125\. These counts identify precisely where history replay is removed and where a guarded text branch remains active\.

The numerical\-stability implementation uses CPU FP64 Adam master parameters and moments, with GPU FP32 LoRA factors and BF16 serialized states\. Its mean write cost is 128\.876 seconds over all 32 sessions and 113\.058 seconds over the matched cost\-profile subset\. Relative to the measured full\-history path, the latter amortizes after approximately 89 reads, assuming zero one\-time writer cost for the full\-history reference\. This 64\-token profile is separate from the earlier 16\-token profile and its 43\-read estimate\. The 44 MiB logical state, the mean 91\.3\-byte supplied clue, and the online latencies represent separate resource dimensions\. A fixed PSS\-readout cache also incurs the original state write and one readout before text\-only use\.