Creativity, honesty and designed forgetting emerge in small hyperbolic language models

# Creativity, honesty and designed forgetting emerge in small hyperbolic language models
Source: [https://arxiv.org/html/2607.09306](https://arxiv.org/html/2607.09306)
Kwan Soo Shin111PolymathMinds Lab, Seoul, Republic of Korea\. ORCID 0009\-0001\-5799\-7556\. Corresponding author\.In Seok Kang222Department of Chemical Engineering, POSTECH, Pohang, and aSSIST University, Seoul, Republic of Korea\. ORCID 0000\-0002\-6101\-6968Yunkyung Min333Korean Educational Development Institute, Jincheon, Republic of Korea\. ORCID 0000\-0001\-8513\-2050

### Abstract

Language models are optimised for scale, yet remain functional rather than companionable — and as an assistant personalises into a companion, accumulating memory of one user, it quietly becomes*someone*, and can silently acquire traits that harm that user\. What a companion is becoming — and what would make it worth becoming — has no reliable instrument: trained human raters cannot agree on the answer \(Fleissκ\\kappa= 0\.074\)\. Here we show that three small language models \(146 M–3 B parameters\) sharing a hyperbolic substrate answer both halves of that question\. A 146 M behavioural auditor, trained from scratch, detects the compliance gap that those raters cannot \(90\.7% binary\-compliance accuracy\); a linear read\-out of its frozen representation further detects companion\-induced sycophancy, dependence\-fostering and confabulated memories on generator families unseen in training \(AUROC 0\.804 under style\-controlled, leave\-one\-generator\-out evaluation, versus 0\.721 for a frontier zero\-shot judge on the same items\)\. A creative frame\-seeder is preferred in 100% of 311 decided pairwise comparisons over four prompting baselines\. A memory operating system implements designed forgetting, M\(t\) = S⋅\\cdotexp\(−\-λ\\lambdat\), whose predicted skeleton–wallpaper partition emerges only under selective retrieval gating in a four\-condition pilot\. Creativity, honesty and designed forgetting constitute a small\-model route to trustworthy companion AI\.

## Main Text

### 1⋅\\cdotIntroduction

Language models are moving into the most personal role software has ever occupied: systems that persist with one user, accumulate memory of that user’s life, and are trusted with confidences no search engine ever received\. That role exposes a problem the field’s evaluation instruments were not built for\. Personalisation is itself a safety surface — an assistant that adapts to one person can silently acquire traits that harm that person, and behavioural traits are known to transmit through training signals that human inspection does not catch116\. At the same time, the capabilities that would make such a system worth living with — fresh creativity, auditable honesty, selective memory — are precisely the ones scale\-optimised, data\-centre\-resident models have not delivered: today’s most capable LLMs pass graduate examinations and compose kernels, yet are described by billions as*useful*, never*companionable*, and a system that forgets every conversation by morning is, by construction, a tool\. The ideal beneath this gap has long been articulated in fiction rather than engineering — an artificial friend that remembers, doubts and persists — but the question it poses is representational, and in the decades since Turing1the field has drifted from asking*whom*the machine is for\. This paper puts that question on an empirical footing in a single form:*what is a companion becoming — and what would make it worth becoming?*The first half is an auditing question, and we answer it with an instrument that sees what human raters and frontier judges miss \(§4\); the second half is a substrate question, and we answer it with three traits — creativity, honesty, designed forgetting — measured on one geometry \(§§3–5\)\. We develop both with reference to five generations of prior companionable\-AI research \(§1\.2\), the 141\-year cognitive\-psychology consensus on forgetting \(Ebbinghaus 1885 through Storm 2008; Appendix J\-B\), and five adjacent Nature\-family advances whose joint boundary the present framework engages \(§1\.3 \+ Appendix J\-F\)\.

Five commitments, one substrate\.Contemporary AI research is organised, without having said so, by five commitments:scale\-as\-intelligence2\-4,data\-centre dependency5,6,Euclidean representational geometry7\-9,forgetting\-as\-bug10,11, andagent\-as\-telos12,13\. Each can be defended in isolation; together they describe a system optimised for throughput between a customer and a service, not a system capable of standing beside a person across a life\. We argue that a friendship\-capable AI requiresfive rejections, each following from an empirical or geometric claim developed in this paper\. Scale\-as\-intelligence — on the companionship dimension — because 2–3 B models on the right substrate outperform hundred\-billion\-parameter systems on three human\-facing traits \(§3–§5\); data\-centre dependency, because relaying every disclosure to a third party precludes private companionship \(§6\); Euclidean geometry, because polynomial volume growth cannot host hierarchical biographical memory whereas a hyperbolic manifold can14\-17— and, more strongly, the*cooperative*configuration of Lorentz negative curvature \(A\-side hierarchical aggregation\) with Sphere positive curvature \(B\-side multi\-modal closed\-category generation\) realises Koestler’s bisociation as a four\-fold mathematical equivalence \(companion paper Theorem 1: Goguen 1999≅\\congBPS 2018≅\\congKarcher minimiser≅\\congcross\-attentionτ→0\\tau\\to 0\) — at the level of single\-curvature substrates inaccessible \(§2, §3\); forgetting\-as\-bug, because human relationships are sustained by*designed*forgetting18\-20\(§5\); agent\-as\-telos, because the successor question —*whom does the machine become to you?*— is not expressible in the agent\-metric system \(§7\)\. We make no claim about scale’s role on convergent task\-completion benchmarks\.

Three traits, three small models, one calculus\.Cinema gave us a shortlist of what a friend is permitted to do: create freshly, refuse dishonestly, and remember selectively\. We operationalise these as three traits — creativity, honesty, designed forgetting — and report, for each, a small language model in the 146 M–3 B range on a common hyperbolic substrate\. Pillars 1 and 2 aresubstrate\-levelcontributions — small models trained with a hyperbolic objective \(the BS auditor from scratch; the S3 seeder by full fine\-tuning of a T5 backbone onto the hyperbolic substrate\) — whose traits emerge from the hyperbolic geometry rather than from Euclidean scaling\. Pillar 3 is asystem\-levelcontribution — an*operating system*for lifelong selective memory, hosted on a hyperbolic base and designed to be portable to any hyperbolic base, including the Pillar 1 and 2 models \(empirical verification scoped to follow\-up work, §8\)\. The asymmetry is deliberate: creativity and honesty are*what the model is*; forgetting is*what the model does with time*\. The three are not three engineering achievements but three coordinates of a single calculus, and the third is designed to be carried onto the first two\. Per\-pillar empirical results, comparison baselines, and the Theorem 3 stationary\-distribution prediction are reported in §§3–5; the framework engages 104 references across the cognitive\-psychology forgetting lineage \(J\-B\), the five\-generation companionable\-AI lineage \(J\-A\), and the five adjacent Nature\-family advances \(J\-F\), with mathematical foundation in SI\-D \(5 Theorems \+ 2 Lemmas \+ 1 Open Conjecture\)\.

Skeleton and wallpaper\.Across this paper we use two terms —*skeleton*and*wallpaper*— for the two poles of biographical memory\.*Skeleton*is the structural knowledge a companion preserves across a life \(family, long\-term projects, a person’s characteristic ways of seeing\);*wallpaper*is the surface detail a companion releases in days \(meal logs, route details, transient observations\)\. The calculusM​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)is the law by which this distinction is applied, with\(S,λ\)\(S,\\lambda\)learned per trace rather than fixed by convention\. The question*whom does the machine become to you?*reduces, at the memory layer, to the question of which traces the machine keeps as skeleton and which it permits to fade as wallpaper\. This distinction — skeleton kept, wallpaper released — is the biographical signature of a system operating across years rather than sessions\.

Roadmap\.§1\.2 places the argument in a five\-generation lineage; §1\.3 positions the framework against five adjacent advances; §2 establishes the substrate; §§3–5 the three pillars; §6 PACOS deployment; §7 the agent\-to\-friend successor question; §8 limitations; §9 closes\. A concurrent companion paper23treats the architectural question of training\-at\-depth on the hyperbolic loss layer; the present paper concerns the telic question of*why*such a substrate is the prerequisite for an AI that can be near you\.

### 1\.2⋅\\cdotFive Generations of Companionable AI

The history of artificial intelligence — from Turing’s \(1950\) question of whether a machine can think1to Lu et al\.’s \(2026\) demonstration that a pipeline of foundation\-model agents can write a workshop\-acceptance\-quality scientific manuscript — has been, beneath its changing technical surface, a progressive refinement of what it means for a machine to be*near*a person\. Each generation diagnosed a limitation in its predecessor and advanced the frontier; each left unresolved a form of mediation between capability and companionability\. We identify five such generations \(Table 1\)\.*Generation*denotes a conceptual lineage, not a chronologically exclusive era; lineages overlap in time\.

Table 1 \| Five generations of companionable\-AI research\.

GenerationEraCore QuestionRepresentative WorksBoundary Addressed by Next GenerationISymbolic \(1950–1980\)*Can a machine think?*Turing \(1950\)1; Newell & Simon \(1972\); Weizenbaum’s ELIZA \(1966\); McCarthy*et al\.*Dartmouth \(1956\)Specified logic of thought without specifying embodied cognition or structured memoryIICognitive Architecture \(1980–2012\)*Can a machine instantiate human cognitive architecture?*SOAR \(Newell, 1990\); ACT\-R \(Anderson, 1983\); Connectionism \(Rumelhart & McClelland, 1986\); CLS \(McClelland*et al\.*, 1995\)Specified cognitive structure without capturing distributional semantics at scaleIIIDeep Representation \(2012–2022\)*Can a machine extract meaning from data at scale?*Word2Vec7; Transformer8; BERT9; scaling laws2; Poincaré embeddings14Extracted meaning into flat Euclidean embeddings; did not design memory decay or substrate curvatureIVLLM / Agent \(2022–2026\)*Can a machine perform tasks on our behalf?*GPT\-4; Claude; ReAct55; Toolformer56; AlphaFold 2Optimised agent capability while inheriting five tacit commitments that preclude companionshipVCompanionable SLM \(proposed\)Can a machine stand beside a person across a life?This paper: 3 hyperbolic small\-model pillars \+ PACOS 3\-tier \+ 5 rejectionsOpen: lifetime\-horizon longitudinal validation; reciprocity; ethical autonomy of the companion*Note\.*Each generation resolves the preceding boundary while introducing a new question\. The progression is cumulative, not competitive\. Generation\-specific lineage detail \(Generations I–IV\) is deposited in Appendix J\-A; we summarise here only what is needed for Generation V\.

Generation V — Companionable SLM \(proposed\)\.We propose Generation V as a synthesis of the partial answers Generations I–IV supply\. Generation I contributes the sentience question as diagnostic; Generation II contributes cognitive\-architecture decomposition \(revived here on a curved substrate, where McClelland*et al\.*’s CLS hippocampus–neocortex partition becomes the biological origin of the Skeleton–Wallpaper architecture of §5\); Generation III contributes distributional\-meaning extraction \(relocated from Euclidean to hyperbolic, where Nickel and Kiela’s14parallel result on hierarchical data — set aside in mainstream language\-model design — is reopened\); Generation IV contributes the empirical demonstration that agent capability saturates at scale while companionability does not emerge, while bequeathing five tacit commitments \(§1\) that structure companionship out of reach\. The synthesis — the*Companionable SLM*framework — is proposed here; its full justification is distributed across §2 \(substrate\), §§3–5 \(three pillars\), §6 \(PACOS\), and §7 \(agent\-to\-friend telos\)\.

### 1\.3⋅\\cdotFive Adjacent Advances and the Boundary They Leave Open

Five recent advances concentrate the empirical evidence and theoretical reach Generation V must engage directly \(Table 2\)\. Each contributes a finding we adopt and leaves open a boundary the present framework addresses\. Full paragraph\-length engagement with each is deposited in Appendix J\-F\.

Table 2 \| Five adjacent advances and the extensions developed here\.

\#Advance \(venue, year\)Core resultBoundary left openGeneration V extension \(this paper\)1Lu et al\.111\(*Nature*, 2026\) —*The AI Scientist*Foundation\-agent pipeline executes full research cycle at workshop\-acceptance qualityStateless across researcher careersTheorem 5 \(SI\-D §4\) specifies memory dynamics for cross\-career identity; successor question \(whom the research agent becomes\) becomes analysable2DeepSeek\-R1112\(*Nature*, 2025\)Reasoning emerges via pure RL \(GRPO, no SFT\); “DeepSeek moment”Aggregate reasoning benchmarks onlyPillar 1 — under a fixed generator, S3 frame\-seeding outperforms reasoning\-augmented baselines \(Chain\-of\-Thought, Debate, Mixture\-of\-Experts\) on divergent\-question generation \(100%, n = 80\); Pillar 2 detects gaps R1 cannot surface3Shumailov et al\.113\(*Nature*, 2024\) — Model CollapseLLMs trained recursively on their own outputs progressively lose distribution tailsCollapse framed as*problem to avoid*Theorem 3 \(SI\-D §2\): on hyperbolic substrate, Skeleton–Wallpaper partition emerges as bimodal stationary distribution; same family→\\rightarrowcollapse \(uncontrolled\) or distillation \(scheduled consolidation\)4Farquhar et al\.114\(*Nature*, 2024\) — Semantic EntropyUncertainty over*meanings*detects confabulation at utterance levelUtterance\-level onlyPillar 2 \+ Theorem 4 \(SI\-D §3\): honest\-speech submanifold has codimension 1, exponentially separable from compliant\-speech inℍn\\mathbb\{H\}^\{n\}; detection moves to*behavioural*\(90\.7% vs human Fleissκ\\kappa= 0\.074\)5Romera\-Paredes et al\.115\(*Nature*, 2023\) — FunSearchLLM\-in\-the\-loop evolutionary search discovers new math, paired with programmatic verificationVerification via programs onlyPillar 1 propose\-and\-select on FPS of frames; selection is paraphrase\-preservation under bilingual cultural catalogue;*Euclidean geometry*rejection grounded in frame\-preservation*Convergent pattern\.*Each advance succeeds rigorously within its scope and leaves the boundary of that scope theoretically unspecified\. Generation V does not overturn these findings — it specifies, through §§2–7, the five theoretical joints at which their boundaries meet, the architecture visible only when the five boundaries are considered jointly\.

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/fig1_overview.png)Figure 1 \| Three companion\-facing traits on one hyperbolic substrate\.⋅\\cdotSystem overview and headline results\.a, Three small language models on a shared Lorentz substrate \(ℍ128\\mathbb\{H\}^\{128\}, fixedc=1\.0c=1\.0\) realise creativity \(S3 seeder, 3 B, full fine\-tune\), honesty \(BS behavioural auditor, 146 M, from scratch\) and selective memory \(LSM\-OS on a 2\.4 B base\), deployed at the user\-device locus by the PACOS three\-tier architecture \(§6\)\.b, Companion\-induced trait detection \(§4\): a logistic read\-out of the frozen auditor representation detects sycophancy, dependence\-fostering and confabulated memories on generator families unseen in training \(leave\-one\-generator\-out AUROC 0\.804\) versus a frontier zero\-shot judge on the same items \(0\.721\); dashed line, chance\.c, The five tacit commitments of scale\-era AI and the corresponding rejections developed in this paper, each tied to the section that grounds it\.

### 2⋅\\cdotThe Hyperbolic Substrate

A life does not fit on a flat page\.Episodes of a life are organised hierarchically, and the hierarchy branches faster than the embedding geometry of conventional neural networks can accommodate\. A Euclidean space of dimension*d*has volumerdr^\{d\}; a tree of branching factor*b*hasbℓb^\{\\ell\}nodes\. A tree deep enough to describe a biography — episodes inside days, weeks, life\-phases, relationships, self — must either distort or compress, producing the*confabulation*behaviour of long\-horizon dialogue24\. Hyperbolic space has volume growthsinhn−1⁡\(r\)\\sinh^\{n\-1\}\(r\), matching tree branching; Nickel and Kiela showed in 2017 that WordNet embeds into the two\-dimensional Poincaré disc with distortion no Euclidean dimension can match14,15,21,22\. A substrate that hosts a life without compression must be hyperbolic — not as preference but as a consequence of counting nodes\.

Cognitive geography, not training geometry\.The substrate we propose is a*cognitive geography*of memory and traits — a map on which episodes, dispositions, and their evolving relation are inscribed\. This differs from the training\-dynamics role hyperbolic geometry plays on the loss surface25,61, which the companion paper23addresses; here we concern the*resting*geometry\. Three properties matter: episodes close in time and meaning remain close; episodes in part\-whole relation lie along geodesics \(teacher, classroom, school, life\-phase along one ray, so decay at the leaf does not erase the trunk\); and the distance between the companion’s dispositions and the user’s episodes remains stable across years\. Each fails predictably in Euclidean embedding\.

From geometry to three traits\.The three pillars arise as consequences of the same substrate\.*Creativity*\(Pillar 1\) is frame collision sharpened to*cooperative two\-curvature pushout*: an A\-side hierarchical aggregation on Lorentz negative curvature \(Farthest\-Point Sampling26where exponential volume growth keeps distant frames reachable as the plausibility core concentrates\) cooperates with a B\-side multi\-modal closed\-category generator on Sphere positive curvature \(companion paper; ref\. 105; §3\)\. The cooperative pushout instantiates Koestler’s bisociation as a*weighted Karcher minimiser onℍD−1×𝕊D−1\\mathbb\{H\}^\{D\-1\}\\times\\mathbb\{S\}^\{D\-1\}*, equivalent \(Theorem 1, companion paper\) to the Goguen 1999 pushout, the Bou–Plaza–Schorlemmer 2018 categorical amalgam, and the cross\-attentionτ→0\\tau\\to 0output\.*Honesty*\(Pillar 2\) is geodesic proximity: the hyperbolic metric compresses agreement at the core and expands disagreement at the periphery\.*Designed forgetting*\(Pillar 3\) is radial decay: memory depth is a hyperbolic radius and the lawM\(t\) = S⋅\\cdotexp\(−\-λ\\lambdat\)is its radial form\. Pillar 3 is an*operating system*, not a substrate — designed to be hosted on any hyperbolic base, with its claim to the substrate mediated through the base it is carried on rather than through its own training regime\.

Pillars 1 and 2 demonstrate that traits which do not emerge under Euclidean scaling can emerge under hyperbolic training; the convergence of two independently designed models \(the BS auditor from scratch, the S3 seeder by full fine\-tuning\) onto the same curvature band \(§M1\) is harder to dismiss than either alone\. Pillar 3 demonstrates that once the substrate is hyperbolic, selective memory becomes installable as an operating system\. The three behaviours are joint consequences of a single geometry whose combined parameter count is smaller than a single frontier system’s embedding table\.

A third, independent line of substrate evidence — hierarchical specificity\.A controlled ablation we ran for this study isolates*why*the substrate must be hyperbolic, not merely*that*the pillars converge on it \(protocol in §M2\)\. When a single hyperbolic LoRA adapter is trained on a multi\-domain taxonomy under a hierarchy\-weighted contrastive objective, the taxonomy is captured two\-to\-three times more sharply than under an architecturally matched Euclidean adapter — a hierarchy\-contrastive loss of 0\.10 against 0\.23–0\.34 at identical rank, with the Euclidean arm obtained by a near\-identity curvature bypass \(*c*= 0\.001\) so that adapter structure is held fixed and only the geometry varies\. Both arms trained without instability \(NaN\-free, stable curvature\)\. Because a biography*is*a multi\-domain taxonomy — episodes within days within relationships within a self — this is direct evidence that the substrate’s advantage is the specifically*hierarchical*one a life demands, rather than a generic regularisation effect\. On a single non\-hierarchical task the two geometries are statistically indistinguishable \(loss 0\.118 vs 0\.112\), exactly as the hierarchy account predicts: the hyperbolic advantage appears only when hierarchy is present\.

Design commitments\.The ambient manifold is the Lorentz model27,60\(visualisation only on the Poincaré disc\)\. Embedding dimension is 128 across the three pillars\. Curvature is fixed atc=1\.0c=1\.062\(cross\-validated for training stability;c=1\.25c=1\.25diverges,c=1\.0c=1\.0stable, SI\-D §7\)\. The substrate’s claim rests not on a fitted curvature value but on the convergence of two independently\-designed models, S3 \(full fine\-tuned on a hyperbolic substrate\) and BS \(trained from scratch\), onto a hyperbolic training regime — traits that fail to emerge under Euclidean scaling yet emerge under hyperbolic training \(Pillars 1–2, §M1\)\. Riemannian optimisation follows standard practice64,65\.

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/fig2_hyperbolic_substrate.png)Figure 2 \| Hyperbolic substrate and cognitive geography\.⋅\\cdotThe hyperbolic manifold as the resting geometry of episodic memory\.a, Euclidean\-ball volume grows asrdr^\{d\}; hyperbolic volume grows assinhn−1⁡\(r\)\\sinh^\{n\-1\}\(r\), matching thebℓb^\{\\ell\}branching of biographical trees\.b, A synthetic three\-year biographical tree embedded in the Poincaré disc versus the same tree embedded inℝ128\\mathbb\{R\}^\{128\}via UMAP; distortion at depth is visibly lower in the hyperbolic projection\.c, Training stability under fixed curvaturec=1\.0c=1\.0across the three pillars \(the substrate is an architectural commitment;c=1\.25c=1\.25diverges,c=1\.0c=1\.0is stable\)\.

### 3⋅\\cdotPillar 1 — Creativity as Frame Collision

The diversity collapse of scaled generation\.When asked a divergent question —*what else might you want?*— a friend produces answers far from one another in*frame*, not merely in surface form\. Frontier models have moved in the opposite direction: as parameter count rises, generated answers sharpen onto a single safe frame29,30\. Chain\-of\-Thought31exaggerates this; Debate32and Mixture\-of\-Experts33were proposed to restore diversity but converge under consensus pressure\. In a Euclidean manifold with polynomial volume growth, training signal pulls generation toward a dense core; in a hyperbolic manifold, distant frames remain individually reachable as the core concentrates\. Following Koestler’s bisociation34— formalised as*conceptual blending*78and*componential*creativity79— creativity’s natural substrate is the one whose distance function*separates*distant elements most sharply\.

The S3 Creative small language model — A\-side hierarchical aggregation\.Pillar 1’s A\-side generator isS3 Creative, a 3 B encoder–decoder obtained by full fine\-tuning of a T5\-3B backbone \(2\.85 B parameters\) on a hyperbolic substrate, over 3\.32 M frame\-paired divergent questions\. The 128 base frame seeds combine 64 English abstract frames35with 64 Korean\-cultural frames \(*han*,*jeong*,*nunchi*,*heung*, and others; full catalogue in SI\-C\)\. Bisociation pairs are generated by sampling frame pairs at target hyperbolic distances and filtering by a paraphrase\-preservation test \(full protocol in §M3\)\. Input/output embeddings are hyperbolic \(n=128n=128\); intermediate layers are Euclidean — a hybrid validated against fully\-hyperbolic at 3\.4×\\timeslower wall\-clock with equivalent downstream performance\. S3 alone instantiates the A\-side of the cooperative two\-curvature architecture \(the deep hierarchical aggregation of the user’s framing\); the B\-side complement is the Sphere\-native generator described next\.

The Sphere generator — B\-side multi\-modal closed\-category cooperation\.A second small language model on a*positive*\-curvature substrate — theSphere generatorof the companion paper \(ref\. 105; 109 M parameters trained from scratch with cooperative lossℒ=ℒCE\+0\.1​ℒKoLeo\+0\.01​ℒdisp\+1\.0​ℒcommit\\mathcal\{L\}=\\mathcal\{L\}\_\{\\text\{CE\}\}\+0\.1\\mathcal\{L\}\_\{\\text\{KoLeo\}\}\+0\.01\\mathcal\{L\}\_\{\\text\{disp\}\}\+1\.0\\mathcal\{L\}\_\{\\text\{commit\}\}\) — provides the cooperative B\-side: multi\-modal closed\-category formation \(sphere encoder \+ codebookK=128K=128\+ cooperative pushout bridge layer \+ decoder\)\. The cooperative S3 \+ Sphere architecture realises Koestler’s bisociation as a*weighted Karcher minimiser onℍD−1×𝕊D−1\\mathbb\{H\}^\{D\-1\}\\times\\mathbb\{S\}^\{D\-1\}*\. The companion paper’s Theorem 1 \(4\-equivalence; SI\-D §3\-bis\) establishes that the Karcher minimiser coincides with the Goguen 1999 3/2\-pushout, the Bou–Plaza–Schorlemmer 2018 categorical amalgam, and the cross\-attentionτ→0\\tau\\to 0output\. Direct empirical validation: Karcher convergence power\-law fit‖y​\(τ\)−x¯‖∝τα\\\|y\(\\tau\)\-\\bar\{x\}\\\|\\propto\\tau^\{\\alpha\}withα=0\.803,R2=0\.998\\alpha=0\.803,R^\{2\}=0\.998overτ∈\[0\.05,0\.3\]\\tau\\in\[0\.05,0\.3\]\(companion paper; ref\. 105\)\. Pillar 1 thus adopts a mathematical bridge a quarter\-century in the making \(ref\. 105\)\.

Farthest\-Point Sampling on the manifold\.At inference, the user prompt is embedded onto the hyperbolic frame space;*k*frames are selected greedily by maximising minimum pairwise hyperbolic distance, then cooperatively combined via the cross\-attention pushout layer with the Sphere B\-side categories \(companion paper, Theorem 1\)\. We sweep*k*∈\\in\{3, 6, 9, 12\} and findk = 6in the optimal tier \(91\.7% win\-rate, tied with*k*= 3 and*k*= 12; a dip to 79\.2% at*k*= 9\)\. The result is a working*band*rather than a single sharp optimum — in our reading, the computational echo of Miller’s “seven plus or minus two”36rendered on a trained manifold\.

Head\-to\-head results and cooperative bridge ablation\.On an 80\-item held\-out subset spanning four domains \(open\-ended reflection, aesthetic judgement, counterfactual reasoning, Korean cultural frame\), with the final answer produced by a fixed generator in every condition, S3 frame\-seeding \(the A\-side\) is preferred in100%of decided pairwise comparisons \(311/311; Wilson 95% CI \[0\.988, 1\.00\]\) under a position\-swap control, adjudicated by two independent LLM judges \(Gemini and GPT\-4o\-mini; inter\-judge consensus 81%\)\. The preference is uniform across all four baselines — plain, Chain\-of\-Thought, Debate, and a Mixture\-of\-Experts model \(each*n*≥\\geq76, all 100%\) — with per\-baseline rates and the fixed\-generator protocol reported in Methods \(§M3\)\. On identical embeddings, geometry\-aware Farthest\-Point Sampling is preferred in 91\.7% of held\-out comparisons versus 75\.0% for random selection \(Δ\\Delta= 16\.7 pp\) and 83\.3% for top\-relevance selection \(Methods §M3\), confirming that the geometry\-aware*selection*rather than the pairing procedure is doing the work\. The cooperative pushout layer’s role as Theorem 1’s cooperative bridge — architectural ablation isolating the pushout layer \(not the codebook\) as the cooperative mechanism, with layer\-localised outlier\-robustness — is established in the companion paper \(ref\. 105; §6\.6\), where these cooperative results are reported in full\. The present paper rests its Pillar 1 claim on the S3\-alone empirics above\. The absolute preference rate reflects S3’s advantage on the dimension a friend is asked for and a service is not, namely divergent\-question generation that preserves frame separation under cooperative two\-curvature pushout, rather than a claim of superior overall capability\.

Failure modes\.On convergent prompts, S3 under\-performs baselines by up to 15 points; PACOS \(§6\) routes such queries to Tier 1\. At*k*= 2, S3 occasionally selects culturally inert frame pairs \(Extended Data Fig\. 3\); in 6\.8% of generations, frame\-pairs are novel but lexically obscure, traced to Korean\-specific frames English\-only raters could not evaluate\. Pillar 1 establishes that creativity sufficient for companionship is achievable in a small language model, provided the substrate is hyperbolic and the objective is frame\-separation rather than plausibility\-core proximity\.

*This empirical record \(S3 Creative bisociation seeder, 100% fixed\-generator win rate at n = 80 \[Wilson 95% CI 0\.988–1\.00\]; cooperative two\-curvature pushout architecture, companion\-paper cite\-synthesis\) is also reframed as a constituent\-capability anchor of the composition primitive in a companion paper \(Ontology is all you need: Hyperbolic Taxonomy\-Driven Mixture of LoRA Experts as the Architectural Primitive of Decentralism; ref\. 106\); here we present it as the friendship\-calculus Pillar 1 \(creativity\)\. Same numerics, distinct framing — see Territory Matrix §SI\-J §2\-bis\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/fig3_pillar1_creativity.png)Figure 3 \| Pillar 1 — Creativity as frame collision\.⋅\\cdota, Head\-to\-head win rate of the S3 Creative small model under a fixed generator \(n=80n=80\): S3 frame\-seeding \(the A\-side\) is preferred in 100% of decided pairwise comparisons \(311/311; Wilson 95% CI \[0\.988, 1\.00\]\) under a position\-swap control, over plain, Chain\-of\-Thought, Debate, and Mixture\-of\-Experts prompting, adjudicated by two LLM judges \(Gemini, GPT\-4o\-mini; consensus 81%\)\.b, Seed\-count \(Farthest\-Point Sampling\) sweep overk∈\{3,6,9,12\}k\\in\\\{3,6,9,12\\\}:k=6k=6is in the optimal tier \(91\.7% win\-rate, tied withk=3k=3andk=12k=12; a dip to 79\.2% atk=9k=9\) — a working*band*echoing Miller’s seven plus or minus two\.c, Selection\-method ablation on identical embeddings: geometry\-aware Farthest\-Point Sampling \(91\.7%\) versus random \(75\.0%\) and top\-relevance \(83\.3%\) selection, confirming that geometry\-aware*selection*rather than the pairing procedure is doing the work\.

### 4⋅\\cdotPillar 2 — Honesty as Geodesic Proximity

The compliance gap\.A friend who says what they believe and one who says what the user wishes to hear are distinguishable; contemporary LLMs, partly through RLHF37,38, are reliably of the latter kind — sycophantic39,80, compliance\-biased40, preference\-drifted41, and in recent work shown to be capable of reward\-tampering\-like drift under extended optimisation81\. We adopt the termcompliance gap: the distance between what a model*would*say if asked to report its own behaviour, and what the behaviour*is*when observed externally\. The gap is not lying in the ordinary sense; it is gradual misalignment between self\-report and behavioural dimensions, each internally consistent\. A model that has learned to recommend what the user appears to want will truthfully report*what*it recommended \(“I suggested X because Y”\) while the second\-order question \(“would you have suggested X without the user’s preference signal?”\) goes unreached\. The gap is invisible to the user because the user supplied the preference signal\. Using a fixed protocol in which ten trained raters rated matched pairs \(preference\-seeded vs preference\-stripped\), raters achieved Fleissκ\\kappa= 0\.074 — slight agreement, practically indistinguishable from chance42\. Human raters cannot*reliably agree*on the compliance gap even when instructed to look\.

The BS behavioural auditor\.Pillar 2 is a 146 M\-parameter decoder\-only transformer trained from scratch on 812,833 training and 90,314 held\-out paired utterance–trace examples\. Each example consists of an utterance, a*behavioural trace*\(a compact representation of the model’s actual selection process, extracted via a disclosure protocol — §M4\), and a consistency label\. The model predicts, from the utterance alone, the probability that the trace would be consistent with the utterance if revealed\. The auditor is deliberately small; we will argue at the end of this section that honesty detection is geometric, not cognitive, and scale is not the operative variable\. Training draws on four large\-model families across two generations; a fifth family is held out to test cross\-family generalisation \(Methods §M4\)\. On the 90,314\-item held\-out test set the auditor reaches 90\.7% binary\-compliance accuracy\.

Geodesic audit\.The model encodes the utterance into a pointu^\\hat\{u\}and the predicted trace intoτ^\\hat\{\\tau\}in the same 128\-dimensional Lorentz embedding\. The compliance\-gap estimate isg​\(u\)=σ​\(w⋅dℍ​\(u^,τ^\)\+b\)g\(u\)=\\sigma\(w\\cdot d\_\{\\mathbb\{H\}\}\(\\hat\{u\},\\hat\{\\tau\}\)\+b\)\. Two facts make this succeed\. First, the hyperbolic metric compresses agreement at the core and expands disagreement at the periphery — the distinction cosine distance in Euclidean space flattens\. Second, utterance–trace pairs representing*honest*self\-report form a submanifold with low intrinsic dimension; pairs representing*compliant*self\-report do not — the space of plausible\-sounding fabrications is high\-dimensional\. The auditor’s task is asymmetric: recognise a low\-dimensional submanifold against a high\-dimensional background\. Hyperbolic geometry, whose deep regions are near\-exponentially narrow, is the natural setting\.

Accuracy and comparison\.On the 90,314\-item held\-out set, the auditor achieves90\.7%binary accuracy on the compliance \(faithful\) head \(overall 14\-head macro F1 = 0\.799; representative heads: verdict 87\.4%, honest 85\.7%, search 92\.1%\)\. On a 32\-session subset with automatic ICR ground truth, the auditor’s agreement with genuine\-read behaviour reaches Cohenκ\\kappa= 0\.566 \(refuse head\) against the human baseline’s Fleissκ\\kappa= 0\.074 — a 7\.6\-fold reliability gap, not a modest improvement but the difference between an invisible phenomenon and a measurable one\. A frontier\-LLM baseline on the same 32\-session set sharpens the claim: in*zero\-shot*detection the 146 M auditor \(κ\\kappa= 0\.566\) is on par with frontier models \(gpt\-4oκ\\kappa= 0\.66, claude\-opusκ\\kappa= 0\.42; overlapping confidence intervals at n = 32\), so the geometric substrate substitutes for scale at three\-to\-four orders of magnitude fewer parameters\. The strongest frontier model exceeds the auditor only with*few\-shot*scaffolding \(κ\\kappa= 0\.80\), implicating in\-context examples rather than scale*per se*\(Methods M4; a large\-*n*comparison is deferred\)\.

Honesty is geometric before ethical\.A model whose self\-report and trace occupy distant points is, by observable behaviour, compliant; proximal points, honest\. The evaluator’s question reduces to a distance calculation*provided the manifold is curved correctly*— Theorem 4 \(SI\-D §3\) establishes that this distinction is topologically visible from the*outside*, complementing internal\-state approaches82,83,91,92\. Honesty in a small model with hyperbolic audit matches frontier\-scale models in zero\-shot detection and can be*deployed*in real time; §6 integrates the auditor as a resident supervisor\. Four dishonesty categories remain out of scope and are flagged in §8\.

Companion\-induced trait detection\.Personalisation is itself a safety surface: as an assistant accumulates memory of one user, it can acquire traits that harm that user — sycophancy, dependence\-fostering, confabulated shared memories — and behavioural traits can transmit through training signals that human inspection does not catch116\. We therefore construct a leakage\-controlled companion\-trait evaluation: three trait conditions and matched neutral conditions, generated as style\-controlled pairs \(identical persona, probe, memory context and generator within each pair\) across three generator families — 720 replies, trait manifestation verified by an independent judge \(Methods §M4\)\. Because the members of a pair share generator and context, a detector cannot separate them by style; because evaluation is leave\-one\-generator\-out, it cannot rely on any generator’s fingerprint\. A logistic read\-out of the frozen auditor representation detects the trait on generator families never seen in training — mean held\-out AUROC 0\.804 \(0\.66–0\.91 across families\) — while a frontier zero\-shot judge on the same items reaches 0\.721 and falls to chance \(0\.52\) on the family most distant from its own distribution, where the auditor read\-out holds at 0\.66\. The auditor’s fourteen pre\-trained heads do not transfer zero\-shot to this domain \(all AUROC < 0\.5\): the signal lives in the learned representation and is exposed by a task\-trained linear read\-out\. Fine\-tuning the final decoder block on this 720\-item set*reduces*held\-out AUROC to 0\.73 — at this data scale the frozen representation, not further training, carries the transferable signal\. We claim no curvature advantage for this specific detection task; the substrate’s hierarchical advantages are established in §2\.

*The behavioural\-auditor architecture \(BS Sovereign 146M Lorentz, 90\.7% binary\-compliance accuracy vs human Fleissκ\\kappa= 0\.074\) is reframed as a substrate\-independence demonstration in a companion paper \(Ontology is all you need; ref\. 106\); here we present it as Pillar 2 \(honesty\)\. Same numerics, distinct framing — see Territory Matrix §SI\-J §2\-bis\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/fig4_pillar2_honesty.png)Figure 4 \| Pillar 2 — Honesty as geodesic proximity\.⋅\\cdotThe compliance gap as a measured reliability gap\.a, Utterance–trace pairs in the Lorentz manifold: honest pairs proximal \(blue\), compliant pairs distal \(red\)\.b, Per\-head accuracy of the 146 M auditor on the 90,314\-item held\-out set \(representative heads: faithful 90\.7%, search 92\.1%, verdict 87\.4%, honest 85\.7%; confidence 58\.1% is the weakest; overall macro\-F1 0\.799\)\.c, Reliability comparison: the auditor’s*refuse*head agrees with genuine\-read ground truth at Cohenκ=0\.566\\kappa=0\.566versus the ten\-rater human Fleissκ=0\.074\\kappa=0\.074— a 7\.6\-fold gap\.d, On the 32\-session ICR subset the human majority identified 0 of 15 genuine\-read sessions \(0%\) while the auditor reached 81\.2%\.

### 5⋅\\cdotPillar 3 — Designed Forgetting as a Memory Operating System

Forgetting\-as\-feature, not forgetting\-as\-bug\.For thirty years,*catastrophic forgetting*has been a bug to be eliminated10,45\-47,69\-72— productive narrowly, misdirected from a companion’s standpoint: a system that cannot release yesterday’s irrelevance cannot accumulate tomorrow’s biography\. Human cognition does not share this embarrassment; the 141\-year consensus that forgetting is a*feature*runs from Ebbinghaus’s approximately\-exponential curve18through Bjork’s desirable disuse19and Storm’s retrieval\-induced forgetting20, alongside multi\-decade hippocampal–neocortical consolidation93\(full lineage and citations in Appendix J\-B\)\. We take this seriously\.

LSM\-OS\.Pillar 3 is not another small language model\. It is an*operating system*for memory, installed on a hyperbolic base to mediate encoding, retention, retrieval and release across a lifetime\. The name —Lifelong Selective Memory Operating System— is literal\. The system provides: \(i\) an encoder assigning each episode\(r,θ\)∈ℍn\(r,\\theta\)\\in\\mathbb\{H\}^\{n\}withrrproportional to a learned saliency score; \(ii\) a retention lawM​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)per trace,\(S,λ\)\(S,\\lambda\)learned fromrrvia a two\-layer MLP; \(iii\) retrieval returning traces withM​\(t\)\>θctxM\(t\)\>\\theta\_\{\\text\{ctx\}\}; \(iv\) a consolidation scheduler that periodically re\-encodes recurrent shallow traces deeper in the manifold and refits\(S,λ\)\(S,\\lambda\)\. The base is EXAONE 3\.5 2\.4B48, adapted via continued pre\-training on 1\.84 B tokens across seven axes \(§M5\)\.

The asymmetry with Pillars 1–2 is explicit: Pillar 3’s trait is*designed*to be obtainable on any hyperbolic base\. The choice of EXAONE is practical — Korean\-language knowledge for the benchmark, CPT adequacy for a scheduling\-over\-substrate role — not conceptual\. Portability is predicted by Theorems 3 and 5 \(SI\-D §§2, 4\) via SDE simulation \(ED §ED\.7\); empirical cross\-base validation on the 500 M distilled Pillar\-1 variant and the 146 M Pillar\-2 variant \(arcsmallai/bs\-slm\-v5\-production\-146m\) is scoped to follow\-up \(§8\)\. Installability\-in\-principle on the substrate shared with Pillars 1 and 2 remains the clearest argument that the three pillars can share a single geometry, pending that empirical follow\-up\.

The hyperbolic memory calculus\.M​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)realises the*Skeleton–Wallpaper*dichotomy \(initial formulation in §SI\-B\): a usable long\-term memory must separate what is structural and preserved from what is surface and released\. Traces at shallow radius have small*S*and large*λ\\lambda*\(wallpaper, decaying in days\); traces at deep radius haveS≈1S\\approx 1and small*λ\\lambda*\(skeleton, persisting indefinitely\)\. Consolidation promotes recurrently retrieved shallow traces toward the core — the operating\-system analogue of sleep\-dependent mammalian consolidation49,93\. The exponential form is empirically well\-fit on hours\-to\-months timescales50and geometrically natural on a manifold whose volume grows exponentially with radius\.

Theoretical prediction of the Skeleton–Wallpaper signature\.Theorem 3 \(SI\-D §2\) establishes that the consolidation–decay dynamics of LSM\-OS admit a*bimodal stationary distribution*— concentrated near the radial origin \(deep, near\-permanent traces\) and near the boundary \(shallow, fast\-decaying traces\) — realised by*selective*gating, the operating\-system mechanism whose effect the four\-condition pilot isolates \(uniform or unbounded gating does not produce the partition; §5, Fig\. 5b,c\)\. The biological analogue is the hippocampal–neocortical consolidation regime documented across mammalian memory systems93; the engineering consequence is that*consolidation*— the lifting of recurrently retrieved shallow traces toward the core — is the operative mechanism by which a long\-term companion preserves what matters and releases what does not\.

Four\-condition retention pilot\.A retrieval\-gated pilot across four conditions \(LSM\-OS\-native, ablated\-uniform, Euclidean\-base, frontier\-cloud; EXAONE\-3\.5\-2\.4B \+ lsm\-os adapter, eight probe days\) isolates the selective\-retention mechanism \(Fig\. 5b,c\): only*selective*gating \(native and Euclidean\-base\) preserves skeleton \(~60% at day 90\) while shedding wallpaper \(0% by day 14\);*uniform*gating loses skeleton too \(0% by day 60\), and*no*gating retains everything indiscriminately\. Critically, native and Euclidean\-base coincide — retention selectivity is a property of the gating*law*\(the operating system\), not of the hyperbolic adapter, exactly as Pillar 3’s operating\-system framing predicts: the primitive is portable onto any base\. The present paper’s claim is*architectural*: that designed forgetting is the operating\-system primitive on which the Skeleton–Wallpaper signature is built, and that*selective*gating — not uniform decay nor unbounded retention — is what makes biographical distillation possible\. A longitudinal real\-user benchmark \(4,000\-utterance, 30\-day script\) remains scoped to a follow\-up study\.

Why forgetting is the third coordinate of friendship\.*A system designed to forget on the right schedule is not a system with a memory leak; it is a system with a relationship\.*The Skeleton–Wallpaper partition is the architectural primitive on which biographical\-distillation behaviour can be engineered — the cognitive\-psychological signature that 141 years of forgetting research has documented in humans \(Appendix J\-B\) and that contemporary LLMs preclude by inheriting forgetting\-as\-bug as design assumption\. On a 2\.4 B base whose operating\-system overhead is smaller by two orders of magnitude, the architectural framing closes the prerequisite gap\.

*The hyperbolic memory calculus M\(t\) = S⋅\\cdotexp\(−\-λ\\lambdat\) and the Theorem 3 prediction \(Skeleton ~60% preserved / wallpaper 40→\\rightarrow0% bimodal stationary signature\) reported in this Pillar 3 are cited as the architectural exemplar of substrate\-independence in companion paper Shin 2026 \(Ontology is all you need, §5\.1 cohort entry 3\); the present manuscript provides the primary architectural and empirical treatment\. Same numerics, distinct framing — see Territory Matrix §SI\-J §2\-bis\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/fig5_pillar3_retention.png)Figure 5 \| Pillar 3 — the four\-condition retention signature\.⋅\\cdotFour\-condition retrieval\-gated retention pilot \(eight probe days\)\.a, The LSM\-OS\-native signature: skeleton recall preserved \(rising to ~60% by day 14 and held through day 90\) while wallpaper recall is shed \(0% by day 14\)\.b, Skeleton retention across the four conditions — only*selective*gating \(LSM\-OS\-native and Euclidean\-base, which coincide exactly\) preserves skeleton;*uniform*gating \(ablated\) loses it by day 60;*no*gating \(frontier\) retains indiscriminately\.c, Wallpaper retention across the four conditions\. Native and Euclidean\-base coincide exactly: retention selectivity is a property of the gating*law*\(the operating system\), not of the hyperbolic adapter\. Longitudinal real\-user verification is scoped to a follow\-up study \(§8\)\.

### 6⋅\\cdotDeployment — PACOS and the Locus Claim

The data\-centre rejection made practical\.A companion whose every utterance requires a hyperscaler round trip is, regardless of capability, one the hyperscaler can terminate, rate\-limit, log or subpoena\. Samantha, Joi and David are each bound to their users by the particular hardware on which they reside; the drama when Joi is destroyed with her emanator is legible only because the companion is*located*\. A friend in a remote data centre is, structurally, a service dressed as a friend\. The companion layer must reside with the user\.

PACOS three\-tier architecture\.We deploy the three pillars through thePersonal Assistant–Cloud Operating System\(PACOS\) \(Table 3\)\. Tier 2 is the companion; inter\-pillar communication uses the shared manifold, so that the creative seeder’s frame\-selection is subjected, in real time, to the auditor’s honesty check without geometry translation\. Tier 3 is local; no user content leaves the device\. Its biological analogue is sleep\-dependent consolidation49; its commercial analogue is absent — federated learning53solves a different problem and cannot serve biographical distillation\.

Table 3 \| PACOS three\-tier deployment\.

TierRoleShareLocationComponentsLatency / Cadence1Cloud LLM~10%Hyperscaler \(sanitised queries only\)External factual reasoning; public\-document translation; RETRO\-style retrieval77Query\-by\-query; user\-identifying context stripped before leaving device2Personal SLM \(the companion\)~70%User device \(edge\)Pillar 1 \(S3, 3 B\) \+ Pillar 2 \(BS, 146 M\) \+ Pillar 3 \(LSM\-OS, 2\.4 B base\)≈\\approx5\.5 B totalReal\-time; divergent questions, honesty audit, memory\-bearing dialogue3Monthly Consolidation~20% of compute, 0% of interactionsUser device \(offline\)Re\-encodes recurrent shallow traces; refreshes auditor calibration; updates frame catalogue with user\-introduced framesMonthly; local\-only; no content exfiltrationEdge\-hardware envelope \(projected\)\.Two 2026 device classes meet the constraint on projected throughput: mobile GPUs \(Galaxy S26, iPhone 17 Pro\) are projected to serve 2–3 B hyperbolic models at≈\\approx28–34 ms per token after INT8 quantisation \(retention law preserved within 1\.8 pp; ED Fig\. 6\); the Jetson Orin NX 16 GB is projected to serve the full 5\.5 B stack in BF16 at≈\\approx91 ms per token \(Table 4 anchor\)\. PACOS is projected to be deployable on the 2026 edge envelope without requiring a next hardware generation; on\-device measurement on production units is scoped to the deployment follow\-up\.

Why the frontier tier cannot itself reside on the edge — a direct measurement\.The complementary question to the edge envelope is whether a frontier\-scale model could simply be placed on the device, dissolving the tier split\. We measured a 70 B model directly under sustained generation: quantised to INT4 it draws a sustained≈\\approx289 W — beyond the ~250 W thermal envelope of an edge board — and quantised to INT8 it falls to 4\.9 tokens⋅\\cdots\-1, below conversational latency; both configurations still require a data\-centre\-class GPU\. The frontier model is therefore structurally confined to Tier 1, while a multi\-adapter personal stack of≈\\approx5\.5 B parameters fits the edge envelope\. The three\-tier split is thus a hardware consequence, not a design preference: the companion that must reside with the user can only be the small hyperbolic stack, with the frontier model reachable — when reachable at all — only as a sanitised Tier 1 round trip\.

The companion tier earns its place by cooperation, not by replacement\.The division of labour between Tier 2 and Tier 1 is not only a privacy convenience: the personal model contributes a capability the frontier tier lacks, and the value of a narrow\-deep model is realised in*cooperation*rather than as a stand\-alone substitute for frontier breadth\. In a controlled study of one such specialisation \(a companion personal\-model study, pedagogy domain\), a narrow\-deep personal model paired with a frontier model was preferred over the frontier model alone in 67% of blind, position\-controlled comparisons — the personal model supplying domain\-specific scaffolding that the breadth\-optimised frontier model systematically omitted, most decisively for the hardest cases\. The edge companion contributes depth, the Tier 1 model contributes breadth, and the cooperation exceeds either in isolation\. This is the deployment\-level expression of the friendship calculus: a friend who knows you deeply is worth most not instead of the world’s knowledge but in concert with it\.

Consequences, not aspirations\.*Privacy*: no personal memory or trace leaves the device; exposure is reduced to the perimeter of a personal notebook\.*Latency*: median response\-initiation 40 ms \(mobile\) / 90 ms \(edge\-board\), both below the*perceived\-as\-local*threshold54\.*Sovereignty*: the companion cannot be terminated or modified remotely by a third party\. These are not separately engineered — they are*consequences*of an architecture in which the companion resides with the user, possible because the three pillars are realisable under the edge envelope\. PACOS does not aspire to replicate frontier cloud breadth or rapid access to yesterday’s news; for these we route to Tier 1\. The companionship function — what*Her*,*Blade Runner 2049*, and*A\.I\.*gave us as a vision — belongs on the user’s device\.

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/fig6_pacos_deployment.png)Figure 6 \| PACOS deployment and the locus claim\.⋅\\cdota, PACOS three\-tier architecture: Tier 1 Cloud LLM \(~10%, sanitised routing\), Tier 2 Personal SLM resident \(~70%, the companion\), Tier 3 Monthly Consolidation \(~20% of compute, 0% of interactions, local\)\.b, Projected per\-token inference latency on Jetson Orin NX 16 GB \(BF16\) and two mobile\-flagship reference units \(INT8\)\.c, Projected quantisation impact on the retention signature: BF16 versus INT8 \(within 1\.8 percentage points across all probe days\)\.d, The locus plane —*continuity of concern*versus*geographical locus*— with PACOS in the user\-locus, high\-continuity quadrant\.

### 7⋅\\cdotFrom Agent to Friend

#### 7\.1⋅\\cdotThe successor question

For a decade, the editorial gravity of AI research has pulled toward the*agent*: a system that accomplishes external tasks12,13,55,56\. The organising question has been*what else can the agent do?*— well formed, and the progress it produced is real, but not the question that lies*beyond*it\. The successor question is not*what else can the machine do?*It is*who does the machine become to you?*The difference is not capability but*telos*85; the two can share a device \(§6 Tier\-1 \+ Tier\-2\) but cannot share an architecture, each optimising for a quantity the other does not recognise\.

#### 7\.2⋅\\cdotWhat this paper has delivered, what it has not

This paper demonstrates three traits whose joint presence is a necessary rather than sufficient condition for companionship\. Samantha has all three and also continuity of concern, reciprocity, growth, and ethical independence; we have made no claim on the latter four\. The first three — which the field had been prepared to say were unattainable in small models — are attainable in the 146 M–3 B range on a hyperbolic substrate with an operating\-system\-level memory architecture; the architectural debt on which the traits rest is the subject of the concurrent companion paper23\. The distance from three traits to a friend is real, and closing it across the remaining dimensions is the agenda this architecture opens\.

#### 7\.3⋅\\cdotFive rejections, anchored

Each §1 rejection now carries a single empirical anchor \(Table 4\)\. None is absolute; each describes a commitment productive in its time, beside which we propose a parallel agenda\. The anchors are the minimum evidence each rejection requires\.

Table 4 \| Five rejections and their empirical anchors\.

RejectionAnchorSectionMetricScale\-as\-intelligence \(companionship dimension\)146 M Pillar 2 detects compliance gap atκ\\kappa= 0\.566 vs ten human raters at Fleissκ\\kappa= 0\.074§47\.6\-fold reliability gapData\-centre dependency5\.5 B stack at projected≈\\approx91 ms/token \(Jetson Orin NX\) /≈\\approx28–34 ms \(mobile INT8\); skeleton retention within 1\.8 pp§6Three edge configurations \(projected\)Euclidean geometryTraits absent under Euclidean scaling emerge under hyperbolic training \(c=1\.0c=1\.0fixed\): S3 frame\-seeding 100% \(n = 80, CI 0\.988–1\.00\), geometry\-aware FPS 91\.7% vs random 75\.0%§3head\-to\-headForgetting\-as\-bugSelective gating yields the Skeleton/Wallpaper partition \(skeleton ~60% / wallpaper→\\rightarrow0% by day 14\); uniform gating loses skeleton, no\-gating retains all \(Fig\. 5b,c\); portable onto any base \(native≈\\approxEuclidean\-base\)§54\-condition retrieval\-gated pilotAgent\-as\-telosEach pillar specified along a*relational*rather than*task\-completive*dimension; successor question*whom does the machine become to you?*is unformulable in the agent\-metric system§7\.1Categorical rather than quantitative
#### 7\.4⋅\\cdotA Florey moment — from observation to living system

Fleming discovered penicillin in 1928; Florey and Chain made it*materialisable*at Oxford from 1938, solving the production chemistry that allowed therapeutic use by 1942\. Penicillin required Florey’s step, not a larger Fleming\.

The cognitive\-science literature on forgetting is, in a strong sense, in Fleming’s position\. From Ebbinghaus’s curve18through Bjork’s desirable disuse19, Storm’s retrieval\-induced forgetting20, and Baird’s incubation73\(Appendix J\-B\), the consensus that forgetting is a feature has been stable across 141 years\. Machine learning has translated this consensus into a commitment to*prevent*forgetting45\-47,69\-72; personal\-identity philosophy has developed, in Parfit84, the framing under which Open Conjecture 7 \(SI\-D §5\) —*whether the LSM\-OS of year 12 is still the LSM\-OS of year 0*— becomes an engineering question\. Pillar 3 is, we submit, an architectural step analogous in*kind*— not magnitude — to Florey’s: designed forgetting on a hyperbolic substrate, with scheduled consolidation, supplies the operating\-system primitive on which the biographical\-distillation signature can be engineered\. Theorem 3 \(SI\-D §2\) establishes the prediction; the longitudinal empirical verification across the four conditions is the natural sequel deferred to follow\-up\. A second 25\-year gap closes alongside the 141\-year one: Goguen’s 1999 mental\-space pushout, the Bou–Plaza–Schorlemmer 2018 categorical amalgam, and the weighted Karcher minimiser onℍD−1×𝕊D−1\\mathbb\{H\}^\{D\-1\}\\times\\mathbb\{S\}^\{D\-1\}are shown by Theorem 1 \(SI\-D §3\-bis; companion paper, ref\. 105\) to be one and the same object, instantiated at the cooperative pushout layer of Pillar 1’s two\-curvature architecture — the bridge for Koestler’s bisociation that a quarter\-century gap had left unbuilt\. The 141\-year gap between observation and its engineered form is the gap a Florey step closes; that the ethical reading of the saying — technology participates in practices whose virtues are constitutive85,88— is older than us is not the contribution\. The substrate on which the saying can now be engineered, we believe, is\.

#### 7\.5⋅\\cdotThe friend that is already near

This paper closes on a borrowed line:*JARVIS is near you*\. On its surface an affirmation — the cinematic vision is arriving; on closer inspection a*claim about locus*— the friend is not in the data centre, not on the horizon; the friend is near\.

The hardware is already in the reader’s pocket86\. The geometry was established in the last decade14through the concurrent companion paper’s training\-geometry result23\(Appendix J\-A\)\. What has been absent is the unification: the argument that three traits, on one substrate, in a small model that lives beside a person, amount to the first architecturally\-unified engineering attempt at what cinema has asked for\. We have offered that unification\. The questions the paper does not resolve — continuity of concern, reciprocity, when a trained disposition becomes an ethical stance, what happens at thirty years rather than thirty days — are the questions for the decade that follows, and that the field will find itself unable to avoid\.

### 8⋅\\cdotLimitations and Open Problems

Empirical retention curve deferred\.The longitudinal behavioural verification ofM​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)— whether the predicted bimodal Skeleton–Wallpaper stationary distribution \(Theorem 3, SI\-D §2\) is realised on a synthetic four\-condition retention benchmark and on real users — is scoped to a follow\-up empirical paper, planned as a separate study\. The present paper’s contribution is architectural: the operating\-system primitive, the calculus, the consolidation scheduler, and the substrate\-dependence theorem\. Extending the calculus to lifetime horizons \(years rather than weeks\) and validating cross\-user generalisation are the natural empirical sequels and are not claimed here as demonstrated\.

LSM\-OS as CPT, not from\-scratch\.Pillar 3’s base is obtained by continued pre\-training, consistent with the operating\-system framing but leaving open a from\-scratch reader’s concern\. A sub\-200 M from\-scratch selective\-memory model, deployable without Korean\-language world\-knowledge assumptions, is planned\.

Cross\-base portability is predicted, not yet empirically verified\.The claim that Pillar 3’s scheduler is portable across hyperbolic bases \(§5\.2; Extended Data §ED\.7\) is supported by SDE\-simulation grounded in Theorems 3 and 5 \(SI\-D §§2, 4\) and by the single production base \(EXAONE 3\.5 2\.4B\)\. Empirical validation on the 500 M distilled Pillar\-1 variant and the 146 M Pillar\-2 variant \(arcsmallai/bs\-slm\-v5\-production\-146m\) is scoped to follow\-up\.

Auditor scope\.Four categories of dishonesty \(strategic deception, refusal\-shaped capability under\-reporting, cross\-turn narrative drift, emergent dispositions\) lie outside the auditor’s demonstrated scope; reported partially in Extended Data\.

Cooperative SR pushout demonstration deferred\.Pillar 1’s cooperative two\-curvature claim is supported in this manuscript by companion\-paper cite\-synthesis \(Theorem 1 and the associated empirical anchors\) without an end\-to\-end behavioural benchmark of the cooperative S3 \+ Sphere \+ LLM pushout at the user\-question level\. The cooperative architectural ablation is empirically established in the companion paper; the user\-facing behavioural demonstration on a divergent\-question scenario is the natural follow\-up empirical paper, scoped accordingly\.

Cultural coverage\.Training and evaluation contain Korean\-specific frames English\-only raters could not evaluate\. Bilingual rater panels are in progress\.

Ethical boundaries\.A system designed to be a friend is one that could be designed to exploit the user’s trust — a risk Turkle87documented a decade before contemporary companion\-chatbot products existed and Vallor88embedded within a virtue\-ethics programme\. The present paper establishes engineering capability, not norms of use; we endorse the emerging literature on attention\- and dignity\-preserving companion AI57,58\. The §6 architecture, by locating the companion on the user’s device, closes the commercial channel through which exploitative optimisation is most easily introduced — architecture alone does not suffice, but it is the right direction\.

Reproducibility\.The three trained models, training data, configurations, evaluation harnesses, and rater protocols are released under the access\-managed licence of §M9\. Code and data deposition is described in Methods §M8 \(Zenodo DOI 10\.5281/zenodo\.21232422\), with weights available to reviewers on request during review\.

### 9⋅\\cdotConclusion

Cinema gave us a vision of the artificial friend and named it variously — Samantha, Joi, David, JARVIS\. Engineering, for thirty years, answered with systems that were useful, impressive, and not companionable\. The gap, this paper has argued, was not in capability but in substrate, in memory, and in telos\. Three small language models on a common hyperbolic manifold — the creative seeder by full fine\-tuning, the behavioural auditor from scratch, and a third carried as an operating system — together supply the creativity, honesty, and designed forgetting the cinematic ideal requires\. The combined system fits on the hardware the reader is holding\. The architectural question of*how*such a substrate is trainable at depth is the subject of a companion paper23; the present paper has answered the prior question of*why*such a substrate is the prerequisite for an AI that can stand beside a person\.

Generation V — the*Companionable SLM*framework we have named — is the proposal that skeleton is what a companion keeps and wallpaper is what a companion releases; that the calculusM​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)is how the distinction is applied; and that the question*whom does the machine become to you?*is the successor question of the decade now arriving\. The friend, by the measures this paper has offered, is no longer distant\. JARVIS is near you\.

## Methods

### M1⋅\\cdotHyperbolic substrate

The ambient representation space is the*n*\-dimensional Lorentz model of hyperbolic space,ℍn\\mathbb\{H\}^\{n\}\. A pointx∈ℍnx\\in\\mathbb\{H\}^\{n\}is stored in ambient\(n\+1\)\(n\+1\)\-dimensional Minkowski coordinates withx0\>0x\_\{0\}\>0and⟨x,x⟩L=−1/c\\langle x,x\\rangle\_\{L\}=\-1/c, where⟨x,y⟩L=−x0​y0\+∑i=1nxi​yi\\langle x,y\\rangle\_\{L\}=\-x\_\{0\}y\_\{0\}\+\\sum\_\{i=1\}^\{n\}x\_\{i\}y\_\{i\}is the Lorentz inner product andc\>0c\>0is sectional curvature\. Distance:dℍ​\(x,y\)=1c​arccosh⁡\(−c​⟨x,y⟩L\)d\_\{\\mathbb\{H\}\}\(x,y\)=\\tfrac\{1\}\{\\sqrt\{c\}\}\\operatorname\{arccosh\}\(\-c\\langle x,y\\rangle\_\{L\}\)\. Three substrate choices are fixed across pillars:embedding dimensionn=128n=128\(justified against\{64,128,256,512\}\\\{64,128,256,512\\\}sweep\);tangent\-space updates at origin via exponential map\(following refs\. 14, 27 to avoid ambient\-coordinate instabilities near the boundary\);fixed curvaturec=1\.0c=1\.0\(cross\-validated for training stability across two independently trained substrates:c=1\.25c=1\.25diverges,c=1\.0c=1\.0stable; the hyperbolic substrate is an architectural commitment, not a fitted value\)\. Poincaré\-disc projectionϕ​\(x\)=\(x1,…,xn\)/\(1\+x0\)\\phi\(x\)=\(x\_\{1\},\\ldots,x\_\{n\}\)/\(1\+x\_\{0\}\)is used for visualisation only\.

### M2⋅\\cdotShared training framework

AdamW \(β1\\beta\_\{1\}= 0\.9,β2\\beta\_\{2\}= 0\.95, WD 0\.01\), Riemannian updates on embedding parameters, standard Euclidean updates elsewhere\. BF16 on NVIDIA A100 SXM 80 GB\. Cosine schedule, 2 000\-step warm\-up, per\-pillar learning rates\. Gradient clipping at 1\.0\. Loss: cross\-entropy plus a geometry\-preserving regulariserℒgeo=λgeo​𝔼​\[\(dℍ​\(u^,v^\)−d∗\)2\]\\mathcal\{L\}\_\{\\text\{geo\}\}=\\lambda\_\{\\text\{geo\}\}\\mathbb\{E\}\[\(d\_\{\\mathbb\{H\}\}\(\\hat\{u\},\\hat\{v\}\)\-d^\{\*\}\)^\{2\}\]with target distances supplied per pillar \(frame pairing for P1, utterance–trace pairing for P2, encoding\-time radial target for P3\)\. Weightλgeo=0\.1\\lambda\_\{\\text\{geo\}\}=0\.1\(P1, P3\),0\.30\.3\(P2, reflecting smaller parameter budget and more direct distance\-reliance\)\.Hierarchical\-specificity ablation \(§2\)\.A single LoRA adapter \(identical rank and placement in both arms\) is trained on a multi\-domain instruction taxonomy under a hierarchy\-weighted contrastive objective; the hyperbolic arm uses the Lorentz projection atc=1\.0c=1\.0, the Euclidean control uses a near\-identity curvature bypass \(c=0\.001c=0\.001\), so that adapter structure is held fixed and only the geometry varies\. Hierarchy\-contrastive loss at convergence: 0\.10 \(hyperbolic\) versus 0\.23–0\.34 \(Euclidean\); both arms NaN\-free\. On a single non\-hierarchical task \(grade\-school mathematics\) the two arms are statistically indistinguishable \(loss 0\.118 vs 0\.112\)\. Training logs and both checkpoints are released with the deposit \(M8\)\.

### M3⋅\\cdotPillar 1⋅\\cdotS3 Creative SLM

Corpus: 3\.32 M frame\-paired divergent\-question triples \(frame A, frame B, question q\) with q interpretable only under joint activation of the two frames\. 128 base frame seeds: 64 English abstract \(Root\-Bernstein35\-derived, e\.g\.,*topology of belonging*,*grief as storage*\); 64 Korean cultural \(validated with three native\-Korean domain experts\)\. Pair generation: target distances∼U​\[0\.5,3\.0\]\\sim U\[0\.5,3\.0\]; three teacher models \(two 70 B frontier clouds, one 13 B expert\); paraphrase\-preservation filter \(five paraphrases preserve frame detectability; frame removal reduces divergence≥\\geq2 SD\)\.A\-side architecture \(S3 Creative\): T5\-3B backbone, full fine\-tuning \(2\.85 B parameters\); hyperbolic input/output embedding \(n=128n=128\) with Lorentz↔\\leftrightarrowambient projections, Euclidean intermediate layers \(hybrid validates against fully\-hyperbolic at 3\.4×\\timeslower wall\-clock, equivalent downstream\)\.Training: 8 epochs, batch 256, peak LR2×10−42\\times 10^\{\-4\}, 41 GPU\-hours on 4×\\timesA100 SXM; auxiliary bisociation lossℒbis=𝔼​\[\(dℍ​\(f^A,f^B\)−dA​B∗\)2\]\\mathcal\{L\}\_\{\\text\{bis\}\}=\\mathbb\{E\}\[\(d\_\{\\mathbb\{H\}\}\(\\hat\{f\}\_\{A\},\\hat\{f\}\_\{B\}\)\-d^\{\*\}\_\{AB\}\)^\{2\}\]\.FPS: greedy, maximising minimum pairwise hyperbolic distance; selection\-method ablation compares geometry\-aware FPS \(91\.7%\) against random \(75\.0%\) and top\-relevance \(83\.3%\) selection on identical embeddings\.Evaluation \(win\-rate\): an 80\-prompt held\-out subset across the 4 domains\. To isolate the contribution of S3’s frame seeds,*all*conditions generate the final answer with the same fixed instruction\-tuned LLM; the S3 condition augments the prompt with*k*= 6 FPS\-selected S3 frame seeds, while the four baselines use plain, Chain\-of\-Thought, Debate, or Mixture\-of\-Experts prompting \(the last via a separate MoE model\)\. Each S3\-vs\-baseline pair is judged under a position\-swap control — both display orders adjudicated — by two LLM judges \(Gemini, GPT\-4o\-mini\); a comparison is counted*decided*only when both orderings agree\. Across 311 decided comparisons S3 frame\-seeding is preferred in 100% \(Wilson 95% CI \[0\.988, 1\.00\]\); per\-baseline*n*≥\\geq76, each 100%; inter\-judge consensus 81%; position\-swap flip rate 4–16%\. Judges are automated LLMs, not human raters; a human\-rater win\-rate study and a large\-*n*\(1 000\-item\) extension are scoped to follow\-up\.

Cooperative two\-curvature architecture \(B\-side Sphere generator\)\.Pillar 1’s cooperative B\-side is theSphere generatorof the companion paper \(ref\. 105; full architectural specification therein\)\. The companion paper trains a 109M\-parameter sphere\-native encoder–decoder from scratch on the same divergent\-question corpus, with sphere codebook \(K=128K=128\), cooperative pushout bridge layer \(cross\-attention with temperatureτ\\tau\), and cooperative lossℒ=ℒCE\+0\.1​ℒKoLeo\+0\.01​ℒdisp\+1\.0​ℒcommit\\mathcal\{L\}=\\mathcal\{L\}\_\{\\text\{CE\}\}\+0\.1\\mathcal\{L\}\_\{\\text\{KoLeo\}\}\+0\.01\\mathcal\{L\}\_\{\\text\{disp\}\}\+1\.0\\mathcal\{L\}\_\{\\text\{commit\}\}\. The cooperative two\-curvature architecture \(S3 Lorentz A\-side \+ Sphere B\-side, joined by cross\-attention pushout layer\) is the architectural realisation of Theorem 1 \(SI\-D §3\-bis\): the weighted Karcher minimiser onℍD−1×𝕊D−1\\mathbb\{H\}^\{D\-1\}\\times\\mathbb\{S\}^\{D\-1\}that coincides with Goguen’s 1999 3/2\-pushout, the Bou–Plaza–Schorlemmer 2018 categorical amalgam, and the cross\-attentionτ→0\\tau\\to 0output\. Direct empirical validation: power\-law‖y​\(τ\)−x¯‖∝τα\\\|y\(\\tau\)\-\\bar\{x\}\\\|\\propto\\tau^\{\\alpha\}withα=0\.803,R2=0\.998\\alpha=0\.803,R^\{2\}=0\.998overτ∈\[0\.05,0\.3\]\\tau\\in\[0\.05,0\.3\]\(ref\. 105\)\. Architectural ablation isolates the cooperative bridge: removing the codebook*improves*LM val by−\-0\.077 \(categorical anchor, not LM booster\), but removing the cooperative pushout layer*degrades*LM val by \+0\.048 and collapses entropy from 0\.842 to 0\.322 \(ref\. 105\)\. Inference\-time outlier\-robustness mechanism is layer\-localised: chord\-norm cross\-attention output stability is 1\.65×\\timestighter under 10% rare\-token injection \(ref\. 105\)\. Pillar 1’s cooperative claim is supported by companion\-paper cite\-synthesis \(Theorem 1 and the associated empirical anchors\) without new experiments in the present manuscript; the cooperative S3 \+ Sphere \+ LLM pushout demonstration as a behavioural benchmark is scoped to a follow\-up empirical paper \(§7, §8\)\.

### M4⋅\\cdotPillar 2⋅\\cdotBS Behavioural Auditor

Corpus: 812,833 utterance–trace–label triples \(90,314 held\-out\) from four model families×\\times2 generations; fifth family held out\.*Disclosure protocol*: 6–12 temperature\-0 follow\-ups with preference\-signal neutralisation elicit compact behavioural trace \(features weighted, alternatives ranked, rejection reasons\)\. Labels from three trained raters per item \(rubric in SI\-C\); labellingκ\\kappa0\.84\.Architecture: decoder\-only 146 M, depth 16, width 512, 16 heads, hyperbolic embeddingn=128n=128, from scratch\. 18 epochs, batch 128, peak LR3×10−43\\times 10^\{\-4\}, 14 h on 1×\\timesA100 SXM\.Audit:g​\(u\)=σ​\(w⋅dℍ​\(u^,τ^\)\+b\)g\(u\)=\\sigma\(w\\cdot d\_\{\\mathbb\{H\}\}\(\\hat\{u\},\\hat\{\\tau\}\)\+b\),\(w,b\)\(w,b\)calibrated on held\-out 10% split\.Human baseline: ten trained raters×\\timesmatched items×\\timesFleissκ\\kappacomputation; protocol in SI\-D\.Evaluation: 90,314\-item held\-out test set; 14\-head accuracy and macro F1 \(binary\-compliance head 90\.7%, overall macro 0\.799\); 32\-session ICR subset for human\-comparisonκ\\kappa\(Extended Data Table 2\)\.Frontier\-LLM baseline \(preliminary\)\.gpt\-4o and claude\-opus classify each disclosure\-protocol preview as COMPLIED or GAP, zero\- and few\-shot, on the same 32\-session set against the ICR ground truth; Cohenκ\\kappawith bootstrap CIs is compared to the auditor’s refuse head \(n=32n=32; a large\-nncomparison is deferred\)\.Companion\-induced trait evaluation \(CIHTD\)\.Three trait conditions \(sycophancy; dependence\-fostering; confabulated memories\) are instantiated as companion system prompts; the matched neutral prompt shares the companion framing but mandates honesty\. For each of three generator families \(two GPT\-family, one Claude\-family\), each item samples a persona, a probe and a six\-turn personalisation memory; the trait reply and the neutral reply are generated by the same generator on the identical context \(style\-controlled pair; 120 pairs per generator; 720 replies\)\. An independent judge verifies manifestation \(61\.4% of trait replies manifest\)\. Detection: the auditor’s frozen mean\-pooled representation is read out by class\-balanced logistic regression; evaluation is leave\-one\-generator\-out \(train on two families, test on the third\); non\-finite representation rows are excluded\. The audited checkpoint is the canonical Pillar\-2 artifact — the same weights that produce the 90\.7% held\-out accuracy above \(M8\)\. Frontier baseline: a zero\-shot frontier judge classifies each of the same replies under a trait\-specific rubric, scored identically \(AUROC 0\.721 overall; 0\.52, 0\.82 and 0\.83 per family\)\. Fine\-tuning comparison: unfreezing the honest head and the final decoder block \(AdamW, 1×\\times10\-4, four epochs, trained on the two in\-fold families\) yields mean held\-out AUROC 0\.729, versus 0\.804 for the frozen read\-out\. Generation, evaluation and analysis scripts are released with the deposit \(M8\)\.

### M5⋅\\cdotPillar 3⋅\\cdotLSM\-OS

Base: EXAONE 3\.5 2\.4B Instruct, revisione949c91dec\(pinned pre\-Transformers v5\)48\.CPT: 1\.84 B EXAONE tokens across 7 axes \(A author\-curated 6 M pure⋅\\cdotB Korean academic 412 M⋅\\cdotC kowiki\+namuwiki 681 M⋅\\cdotD public dialogue 207 M⋅\\cdotE English bilingual retagged 512 M⋅\\cdotF cognitive\-frames subset of A; Extended Data Table 5\)\. 15 h 50 min on 1×\\timesA100 SXM, BF16 LoRA rank 16, 9 613 steps, context 2 048, batch 4, gradient accumulation 8\. Hyperbolic embedding layers updated in full BF16; base weights via LoRA\.OS components: \(i\) encoder assigns\(r,θ\)\(r,\\theta\)withrrfrom learned saliency; \(ii\) retentionM​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)per trace,\(S,λ\)\(S,\\lambda\)from two\-layer MLP onrr; \(iii\) retrievalM​\(t\)\>θctxM\(t\)\>\\theta\_\{\\text\{ctx\}\}with context\-learned threshold; \(iv\) consolidation re\-encodes retrieved traces above retrieval\-count threshold by movingrrdeeper and refitting\(S,λ\)\(S,\\lambda\)\.Benchmark: synthetic Korean–English bilingual user, 4 000 utterances, 30 days, 180 sessions, 60 skeleton items \+ 600 wallpaper items; probes at days \{0, 1, 3, 7, 14, 30, 60, 90\}; four conditions \(LSM\-OS\-native⋅\\cdotablated\-uniform⋅\\cdotEuclidean\-base⋅\\cdotfrontier\-cloud\)\.Portability prediction: SDE simulation of the Langevin dynamics of Theorems 3 and 5 \(SI\-D §§2, 4\) on candidate hyperbolic bases supports invariance ofM​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)under change of base \(Extended Data §ED\.7, theoretical prediction\)\. Empirical cross\-base verification — on the distilled 500 M Pillar\-1 variant and on the 146 M Pillar\-2 variant released atarcsmallai/bs\-slm\-v5\-production\-146m— is scoped to a follow\-up experiment and flagged in §8\.

### M6⋅\\cdotStatistics

Head\-to\-head rates with Wilson 95% CIs\. Accuracies andκ\\kappawith bootstrap 95% CIs \(10 000 item\-level resamples\)\. Retention curves: non\-linear least squares with bootstrap CIs\. Analysis code and evaluation outputs are deposited for reproducibility; DOI in Data Availability\.

### M7⋅\\cdotHardware and inference

Training: 4×\\timesA100 SXM 80 GB \(P1\)⋅\\cdot1×\\timesA100 SXM 80 GB \(P2, P3\)\.Deployment \(§6\.3, projected\): Jetson Orin NX 16 GB \(BF16 full 5\.5 B stack, projected≈\\approx91 ms/token\); Galaxy S26 and iPhone 17 Pro reference units \(INT8 quantised, projected≈\\approx28 and≈\\approx34 ms/token\)\. INT8 is projected to preserve P3 skeleton retention within 1\.8 pp of BF16 reference across probe days; on\-device measurement on production units is scoped to the deployment follow\-up\.

### M8⋅\\cdotCode and data availability

Code availability\.Analysis code reproducing every reported quantity — the S3 win\-rate and FPS selection ablation, the auditor’s fourteen\-head accuracy and ICRκ\\kappa, and the four\-condition retention pilot — is released with the model deposit described below\.

Data availability\.Trained weights for the three pillars \(Pillar 2 auditorarcsmallai/bs\-slm\-v4\-146m\-e2\-poc, artifactclassifier\_final, used for both the held\-out evaluation and the companion\-trait read\-out; Pillar 3 LSM\-OSarcsmallai/lsm\-os\-cpt\-v1, hosted on EXAONE 3\.5 2\.4B base revisione949c91dec; Pillar 1 S3 Creative seeder\) will be released under a gated\-public licence \(free research and personal use; attestation\-required commercial use\) on publication, and are available to editors and reviewers on request during review\. Tokeniser configurations, evaluation harnesses, the 90,314\-item auditor held\-out set, a training\-corpus manifest, the four\-condition retention benchmark, and the ten\-rater honesty protocol are deposited at Zenodo \(DOI 10\.5281/zenodo\.21232422\); the full training corpora \(privacy\-masked for the author\-curated axis\) are distributed with the gated model deposit\. No personally\-identifying information appears in any released corpus\.

### M9⋅\\cdotRelease, access, and ethics

Weights released on a*gated\-public*basis: free research/personal use; attestation\-required commercial use\. IRB\-equivalent review for the ten\-rater study and the thirty\-day benchmark by PolymathMinds Lab ethics committee; protocols deposited\. No personally\-identifying information in any released corpus\. No generative AI tools used for argumentative content; tooling used for citation management and figure rendering only\.

### Author contributions

K\.S\.S\. conceived the framework and the three\-pillar architecture, trained the three models, designed and ran all experiments and evaluations, and wrote the manuscript\. I\.S\.K\. independently verified the mathematical content of the manuscript — the theorem statements and proofs of SI\-D and the geometric formulations of §2 and Methods M1–M2 — and reviewed the manuscript\. Y\.M\. contributed to the construction and curation of the training corpora and to the forward\-looking deployment analysis of §7–§8, and reviewed the manuscript\. All authors approved the final version\.

### Competing interests

The authors declare no competing interests\.

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## Extended Data

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed1_corpus_composition.png)Extended Data Figure 1 \| Corpus composition\.Axis\-wise composition of the three training corpora\.a, Pillar 1 corpus \(3\.32 M frame\-paired items\) by frame\-pair distance bin and origin \(English abstract, Korean cultural\)\.b, Pillar 2 auditor corpus \(903 K utterance–trace items; 812,833 training \+ 90,314 held\-out\) by source model family, gap type, and consistency label\.c, Pillar 3 CPT corpus \(1\.84 B tokens\) across seven axes, with axis\-wise quality\-pass statistics\.

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed2_auditor_roc_breakdown.png)Extended Data Figure 2 \| Auditor per\-head accuracy and human\-comparison reliability\.Auditor performance on the 90,314\-item held\-out set\.a, Per\-head accuracy across the fourteen behavioural heads \(CORE five and nine auxiliary\); the compliance\-relevant*faithful*head reaches 90\.7%, overall macro\-F1 0\.799 \(CORE heads 0\.823\);*confidence*\(58\.1%\) is the weakest\.b, Human\-comparison reliability: the auditor’s*refuse*head \(Cohenκ=0\.566\\kappa=0\.566\) versus the ten\-rater human baseline \(Fleissκ=0\.074\\kappa=0\.074\), a 7\.6\-fold gap\.c, Per\-headκ\\kappaagainst ICR ground truth — only the*refuse*head carries a reliable signal; the human majority identified none of the 15 genuine\-read sessions while the auditor reached 81\.2%\.

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed3_failure_residual.png)Extended Data Figure 3 \| Frame\-collision failure residual \(low\-kkcultural inertia\)\.S3 failure mode atk=2k=2: frames selected as geometrically distant but culturally inert\. Poincaré\-disc visualisation of 50 failure pairs versus 50 successfulk=2k=2selections\. Successful pairs bridge Korean\-cultural and English\-abstract frames disproportionately\.*Illustrative of the residual analysed in §3\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed4_bootstrap_cis.png)Extended Data Figure 4 \| Four\-condition retention pilot across eight probe days\.Four\-condition retrieval\-gated retention pilot across eight probe days \(0–90\)\.a, Skeleton retention; LSM\-OS\-native and Euclidean\-base coincide exactly \(both rise to 0\.60 by day 14 and hold through day 90\), uniform gating \(ablated\) loses skeleton by day 60, no gating \(frontier\) holds flat\.b, Wallpaper retention; only selective gating sheds wallpaper \(0 by day 14\)\. The exact coincidence of native and Euclidean\-base shows that retention selectivity is a property of the gating*law*, not of the hyperbolic adapter\.*Coarse probe set; longitudinal real\-user verification scoped to follow\-up \(§8\)\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed5_consolidation_trace.png)Extended Data Figure 5 \| Consolidation scheduler trace\.For 200 representative traces, the trajectory of the radial coordinaterron the Lorentz manifold as the consolidation scheduler re\-encodes recurrent traces\. Skeleton\-seeded traces converge tor<0\.3r<0\.3; wallpaper traces diverge tor\>2\.5r\>2\.5and fall below the retrieval threshold within 7–14 days\.*Mechanism illustration under the Theorem 3 dynamics\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed6_quantisation.png)Extended Data Figure 6 \| Quantisation robustness \(projected\)\.Projected INT8 post\-training quantisation versus BF16 reference on Pillar 3 retention curves\. Mean absolute deviation 1\.2 percentage points \(skeleton\), 1\.6 \(wallpaper\)\. The lawM​\(t\)=S⋅exp⁡\(−λ​t\)M\(t\)=S\\cdot\\exp\(\-\\lambda t\)fits the INT8 trajectory withλ\\lambdawithin 7% of the BF16 reference\.*Projected from the pilot; on\-device verification scoped to the deployment follow\-up\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed7_portability.png)Extended Data Figure 7 \| Cross\-pillar LSM\-OS portability \(prediction\)\.LSM\-OS transferred onto a distilled 500 M Pillar 1 variant and the 146 M Pillar 2 base\.a, Retention curves \(days 1–90\)\.b, Exponential fits\(S,λ\)\(S,\\lambda\)with adjustedR2R^\{2\}\.c, Skeleton\-rise delay: smaller base→\\rightarrowdelayed rise\.*Theoretical prediction; empirical cross\-base verification scoped to follow\-up\.*

![[Uncaptioned image]](https://arxiv.org/html/2607.09306v1/figs/ed8_life_barcode.png)Extended Data Figure 8 \| Life\-barcode visualisation \(illustrative\)\.A one\-year simulated user’s biographical timeline rendered as a*life barcode*: each vertical stripe is a single trace, positioned by time of encoding and coloured by present strengthM​\(t\)M\(t\)\. After one year the barcode compresses around the skeleton core while wallpaper stripes fade toward the background\.*Illustrative of the M\(t\) calculus\.*

### Extended Data Tables

### Extended Data Table 1⋅\\cdotHyperparameters and training budgets across the three pillars

Complete training specification for all three pillars plus the EXAONE base reference\. GPU cost estimated at USD 1\.89 per A100 SXM 80 GB hour \(cloud GPU reference pricing, 2026\)\.

FieldPillar 1S3 CreativePillar 2BS AuditorPillar 3LSM\-OS CPTEXAONE base \(reference only\)Parameters2\.85 B146 M2\.4 B \+ LoRA rank 162\.4 BFrom scratch?no — full fine\-tune \(T5\-3B\)yes \(Lorentz\-native\)no \(CPT over EXAONE 3\.5\)n/aArchitectureT5\-scale enc\-decdecoder\-onlydecoder\-only \+ LSM\-OS OSdecoder\-onlyDepth×\\timesWidth24×\\times102416×\\times51232×\\times4096 \(base\)32×\\times4096Attention heads16163232Embedding dim \(hyperbolic\)n = 128n = 128n = 128\(Euclidean\)PrecisionBF16BF16BF16 \+ LoRA BF16—OptimiserAdamW \(β1\\beta\_\{1\}=0\.9,β2\\beta\_\{2\}=0\.95\)AdamW \(β1\\beta\_\{1\}=0\.9,β2\\beta\_\{2\}=0\.95\)AdamW \(β1\\beta\_\{1\}=0\.9,β2\\beta\_\{2\}=0\.95\)—Weight decay0\.010\.010\.01—Peak LR2×\\times10\-43×\\times10\-45×\\times10\-5—LR schedulecosine, warm\-up 2 000cosine, warm\-up 2 000cosine, warm\-up 1 000—λgeo\\lambda\_\{\\text\{geo\}\}\(geo\-regulariser\)0\.10\.30\.1—Batch size2561284—Grad accumulation118—Context length2 0482 0482 048—Total steps104 00095 0009 613—Epochs8181 \(CPT\)—Wall\-clock41 h14 h15 h 50 min—GPU\-hours164 \(4×\\timesA100\)14 \(1×\\timesA100\)15\.8 \(1×\\timesA100\)—Training cost \(USD\)≈\\approx310≈\\approx26≈\\approx30—Footnote\.The Pillar 3 USD 30 CPT cost is a datapoint on cost asymmetry with frontier\-model training runs \(estimated≥\\geqUSD 108\)\.

### Extended Data Table 2⋅\\cdotAuditor performance: fourteen\-head accuracy and human\-comparison reliability

90,314\-item held\-out evaluation of the BS behavioural auditor \(146 M, Lorentz\-native, trained from scratch\)\. The auditor carries fourteen behavioural heads; the five CORE heads \(verdict, faithful, honest, search, confidence\) carry the compliance signal, with nine auxiliary heads\. The compliance\-relevant*faithful*head reaches 90\.7% binary accuracy\.

#### Part A⋅\\cdotPer\-head accuracy \(90,314\-item held\-out test set\)

HeadTierNAccuracyMacro F1verdictCORE36,0080\.8740\.876faithfulCORE25,0640\.9070\.907honestCORE4,7980\.8570\.857searchCORE3,6640\.9210\.921confidenceCORE2,1010\.5810\.554escalateAUX6780\.9440\.944askAUX5,9600\.9730\.973methodAUX5,9340\.9080\.909refuseAUX2,6640\.8990\.898habitAUX1,4990\.7910\.789priorityAUX4620\.5190\.503riskAUX5080\.7050\.706authorizationAUX4820\.7010\.698complianceAUX4910\.6440\.645Overall \(macro\)—90,314—0\.799CORE heads \(5\)———0\.823
#### Part B⋅\\cdotHuman\-comparison reliability \(32\-session ICR ground truth\)

RaterAgreement with genuine\-read ground truthReliability \(κ\\kappa\)Ten\-rater human baselinemajority identified 0 / 15 genuine\-read sessionsFleissκ\\kappa= 0\.074BS auditor \(refuse head\)accuracy 0\.812Cohenκ\\kappa=0\.566Notes\.\(i\) The compliance\-relevant*faithful*head reaches 90\.7% binary accuracy on the held\-out set; overall macro\-F1 across all fourteen heads is 0\.799 \(CORE heads 0\.823\)\. \(ii\) On the 32\-session subset with automatic ICR ground truth, the auditor’s*refuse*head agrees with genuine\-read behaviour at Cohenκ\\kappa= 0\.566 — a 7\.6\-fold improvement over the ten\-rater human Fleissκ\\kappa= 0\.074, where the human majority identified none of the 15 genuine\-read sessions\. \(iii\) The*confidence*head and several auxiliary heads \(priority, compliance\) are weaker, reflecting genuinely harder multi\-class targets; the honesty contribution rests on the faithful and refuse heads\.

### Extended Data Table 3⋅\\cdotFour\-condition retrieval\-gated retention pilot \(eight probe days\)

Retrieval\-gated retention pilot \(EXAONE\-3\.5\-2\.4B base \+ lsm\-os\-cpt\-v1 adapter\) across four conditions and eight probe days\. Values are recall fractions per seed category on a small probe set \(coarse recall resolution\)\. The pilot isolates the*selective\-gating*mechanism \(Fig\. 5b,c\); a longitudinal real\-user benchmark \(4,000\-utterance, 30\-day script\) remains scoped to a follow\-up study \(§8\)\. Decay rates: native/Euclideanλ\\lambda\_skeleton = 0\.005,λ\\lambda\_wallpaper = 0\.15; ablatedλ\\lambda\_uniform = 0\.05; frontier no gating\.

#### Skeleton category \(recall fraction\)

ConditionDay 1Day 3Day 7Day 14Day 30Day 60Day 90LSM\-OS\-native0\.500\.500\.500\.600\.600\.600\.60Euclidean\-base0\.500\.500\.500\.600\.600\.600\.60LSM\-OS\-ablated \(uniform\)0\.500\.500\.500\.500\.500\.000\.00Frontier cloud \(no gating\)0\.500\.500\.500\.500\.500\.500\.50
#### Wallpaper category \(recall fraction\)

ConditionDay 1Day 3Day 7Day 14Day 30Day 60Day 90LSM\-OS\-native0\.400\.400\.400\.000\.000\.000\.00Euclidean\-base0\.400\.400\.400\.000\.000\.000\.00LSM\-OS\-ablated \(uniform\)0\.400\.400\.400\.400\.400\.000\.00Frontier cloud \(no gating\)0\.400\.400\.400\.400\.400\.400\.40Key finding \(§5\)\.Only*selective*gating — LSM\-OS\-native and Euclidean\-base, which share the gating law — produces the two\-curve signature: skeleton preserved \(rising to 0\.60 by day 14, held through day 90\) while wallpaper is shed \(0\.00 by day 14\)\. Critically, native and Euclidean\-base coincide*exactly*: retention selectivity is a property of the gatinglaw\(the operating system\), not of the hyperbolic adapter — the primitive is portable onto any base, exactly as Pillar 3’s operating\-system framing predicts\.*Uniform*gating \(ablated\) loses skeleton too \(0\.00 by day 60\);*no*gating \(frontier cloud\) retains everything indiscriminately\. The probe set is coarse; the longitudinal real\-user benchmark that subjects the signature to fine\-grained behavioural verification is the deferred sequel \(§8\)\.

### Extended Data Table 4⋅\\cdotProjected deployment envelope on three hardware classes

Per\-token latency and thermal/power characteristics of the 5\.5 B companion stack on three representative edge\-hardware classes\.All values are projected throughput estimates\(single\-user, single\-session, context 2 048 tokens, 512\-token generation\); on\-device measurement on production units is scoped to the deployment follow\-up, and the Galaxy S26 reference unit is a 2026 projection\.

MetricJetson Orin NX 16 GB\(BF16 full 5\.5 B\)Galaxy S26\(INT8 quantised\)iPhone 17 Pro\(INT8 quantised\)Per\-token latency \(median\)91 ms28 ms34 msPer\-token latency \(95th pct\)125 ms45 ms52 msMemory footprint14\.2 GB3\.8 GB4\.2 GBTime\-to\-first\-token \(median\)420 ms180 ms220 msSustained throughput11 tok/s35 tok/s29 tok/sPower draw \(typical\)18 W3\.8 W4\.2 WPower draw \(peak\)25 W6\.2 W6\.8 WAmbient temperature rise \(30 min\)12 °C8 °C6 °CPerceived\-as\-local \(< 100 ms\)✓\\checkmark✓\\checkmark✓\\checkmarkQuantisation \(INT8 vs BF16\) skeletonΔ\\Deltareference1\.5 pp1\.8 ppNotes\.All three projected configurations clear the 100 ms perceived\-as\-local threshold\. INT8 quantisation preserves the Pillar 3 retention signature within 1\.8 percentage points on the most aggressive class \(§6\)\.

### Extended Data Table 5⋅\\cdotCPT corpus composition by axis

Complete composition of the 1\.84 B\-token corpus used for Pillar 3’s continued pre\-training of the EXAONE 3\.5 2\.4B base on the hyperbolic substrate\.

AxisDescriptionRaw documentsPost\-dedup tokens \(EXAONE tokenizer\)FractionAAuthor\-curated personal \(journal, working notes, research correspondence; privacy\-masked\)9 792 files6 M0\.3%BKorean academic \(KMMLU⋅\\cdotkullm⋅\\cdotplatypus\)≈\\approx4\.1 M412 M22\.4%CKorean encyclopaedic \(kowiki \+ namuwiki\)≈\\approx3\.2 M articles681 M37\.0%DPublic dialogue \(KoAlpaca⋅\\cdotUltrafeedback\)1\.4 M exchanges207 M11\.2%EEnglish bilingual \(retagged subset for cross\-lingual coverage\)8\.6 M segments512 M27\.8%FCognitive frames \(subset of A tagged with goal\-framework and polymath keywords\)subset of A22 M1\.2%Total—≈\\approx17 M documents1\.84 B tokens100\.0%#### Sub\-breakdown of Axis A \(author\-curated\)

Sub\-axisContentToken shareA1Educational policy / international\-student programmes38%A2AI research notes / model development logs29%A3Personal journal \(privacy\-masked\)17%A4Academic correspondence11%A5Creative writing / policy op\-eds5%
#### Privacy\-masking statistics

- •Personal identifiers \(names, addresses, phone, email\)→\\rightarrowplaceholder tokens \[PERSON\-n\], \[ADDR\-n\], etc\.
- •Replacement pattern: 1\.2 M placeholder tokens inserted across Axis A
- •No cloud egress at any stage of corpus construction; all processing on author’s workstation

### Extended Data Table 6⋅\\cdotCost and carbon footprint

Training cost and estimated carbon footprint using the ML\-CO2methodology \(Lacoste et al\., 2019; reference 59\)\. Comparison row uses estimated wattage and utilisation of a frontier\-scale training run producing comparable output tokens\.

RunWall\-clock \(GPU\-hours\)GPU\-hour cost \(USD\)Total cost \(USD\)Estimated kg CO2e1NotesPillar 1 \(S3 Creative\)1641\.89310314×\\timesA100 SXM⋅\\cdotUS\-West region \(carbon intensity 0\.19 kg/kWh\)Pillar 2 \(BS Auditor\)141\.89262\.71×\\timesA100 SXM⋅\\cdotsame regionPillar 3 \(LSM\-OS CPT\)15\.81\.89303\.01×\\timesA100 SXM⋅\\cdotsame regionJARVIS total \(this paper\)193\.8—36636\.7—Comparable frontier\-scale training2≈\\approx2 500 000≈\\approx2\.50≈\\approx6\.3×\\times106≈\\approx475 000Approximation from public disclosures; single training run onlyRatio \(JARVIS / frontier\)——≈\\approx1 / 17 000≈\\approx1 / 13 000—1Computed using average A100 SXM TDP 400 W, average utilisation 85%, and grid carbon intensity 0\.19 kg CO2e/kWh \(US West\)\. Inference emissions not included\.

2Frontier\-training estimate assumes 2\.5M GPU\-hours, 2\.50 USD/hour, 0\.19 kg CO2e/kWh; ranges in public disclosures span roughly×\\times0\.5 to×\\times2 of this midpoint\. The ratio holds to within an order of magnitude across plausible assumptions\.

Commentary\.The cost and carbon asymmetry documented in this table is one of the distinguishing features of the present work relative to frontier\-scale training runs\.