A cognitive architecture for French Hangman

0Summary

1Thesis

Performance is not cognition. A program that wins at Hangman by consulting a dictionary performs; it does not reason. OMEGA takes the opposite as its founding constraint.

Hangman is an ideal test bed for this distinction. The trivial solution — filter the dictionary by the revealed pattern, score letters by the cohort's frequency — reaches ~95–98 %. But it says nothing about understanding: it knows French by heart. OMEGA forbids itself this crutch (grey cheat, switches A1/A2/A3 kept OFF) and asks: how far can a cognition that is not allowed to read the answer go?

"Without reading the dictionary to choose a letter, can one reach the oracle?" — The measured answer is: to within a few points, yes.

The project's central answer: starting from ~2.6 % (first weeks of v0.07), pure cognition reaches ~90 %, and with a cheat-free declaration system, 97.5–98.8 % — against an oracle ceiling of 98.7 %. The remaining gap is not a failure of cognition: it is the language's irreducible ambiguity (a /o/ can be spelled o, au, eau — only the memory of the exact word decides).

2The task & the doctrine

The game: guess a French word of 7 or more letters, letter by letter, within an error budget. On each turn, the engine sees the board (revealed positions) and proposes a letter.

2.1 — Cap §43: the golden rule

No cognitive module reads currentWord beyond the revealed positions. The upward direction (deciding) sees only what is revealed; the downward direction (learning) operates after the game, on the now-legitimate complete word. Reading the answer is only cheating in the upward direction.

2.2 — What is allowed, what is not

• The lexicon is forbidden in letter-scoring (upward). It is allowed for the cohort-based DECLARE (board-derived) and post-game learning (downward). A1/A2/A3 = injection of lexical frequency into scoring = grey cheat, OFF.
• w.p (the pronunciation) is a legitimate input under the "heard word" premise (proto-language, M4_PHON_USE_P) — just as one knows the sound of a word one is trying to spell.
• R66: no module is enabled by default without a falsification test (bypass + paired multi-seed statistics).

3Method

Experimental discipline is the heart of the project — more so than any particular module.

• Measure first. Every architectural question is settled empirically (paired A/B/C, multi-seed), never by conviction.
• Deterministic harness. Online learning + predictive coding made the baseline non-reproducible; the harness was made deterministic (re-seed before init → deterministic bPC weights; reset of the θ state; θ deployment target reset; game RNG aligned). Without this fix, all the Δ were noise.
• Falsification (R66). A module is kept only if, OFF, it is inert (byte-identical baseline) and, ON, it shows a measured contribution. Otherwise it is reverted — even if it "seems" right.
• Isolation. All prototyping on disposable copies; the build is never modified without an order.
• Amplitude AND direction. A fix can restore the correct direction of a signal while appearing modest in amplitude (structural damping) — one must judge both.

4The architecture

OMEGA is a dual Möbius pipeline: a direct circuit (upward, perception → decision) and a mirror circuit (downward, deconstruction toward proto-language). In practice, the P2 mirror remains largely disconnected; the power comes from the direct circuit and its couplings.

4.1 — The substrate & the five levels

The substrate is hyperdimensional (HRR/VSA, Plate 1995): 1024 dimensions for the concept (SDIM), 512 for the lexical (LDIM). Five upward levels:

• M1 — perception: binds position and letter by circular convolution (HRR). A rich representation that tracks reveals and discriminates words.
• M2 — zones (4×4): reduces M1 to 16 zones. historical flaw: the absolute value + averaging throws away the sign/phase → in practice M2 encodes only length. Root cause of a concept collapse (fixed by wiring the concept onto M1).
• M3_d — concept (12 cells, 1024D): a bidirectional competitive autoencoder (bPC, DBPC/Qiu 2025 blueprint) now encoding from M1 (rich), plus a reward-learned readout.
• M4 — lexical/letter: converts the concept and the routes into per-letter scores.
• M5 — decision: picks the letter, with a margin (gap) that measures confidence.

4.2 — Two routes, one arbiter

In line with the dual route of reading (Coltheart, DRC): a spelling route and a phonological route (in SAMPA, from w.p) reason in parallel. The OS v07 arbitrates between them to decide. A salience layer (M_S) fuses the concept into scoring. The whole is regulated by bounded online learning (4 safeguards).

Beyond two routes — precisely. This spelling⟷phonology arbitration is the one for Hangman. The derived corrector (§10) makes three routes reason — spelling, phonology and grammar — but they combine through distinct mechanisms, not a single uniform μ: the OS arbitrates spelling⟷phonology in the speller, grammar merges via a priority cascade (the FP=0 red wins at the same token), and agreement via OS arbitration of the subject in turn arbitrates its own sub-routes (nearest noun · head before "de" · outside-PP · LM coherence). The two-route DRC describes Hangman; OMEGA taken as a whole arbitrates more — through several arbitration paths, not one. A result specific to the project, unborrowed.

5Declarations & the NEO system

Pure cognition plateaus at ~90 %: excellent on what it has seen, limited on the never-encountered word. Declarations close the gap by proposing a whole word when confidence is high. The manual (lexical) declare reaches 98.8 % — but reads the dictionary. The project therefore built an emergent, cheat-free declare, culminating in the NEO system (phase 46):

NEO is additive (OFF-inert, byte-identical baseline), modifies none of the pre-existing declarations, and remains cheat-free by construction: recall tied to the revealed only, masked assembly, downward learning.

6Crossing is not summing — nor multiplying

A central lesson, long misapplied. Combining two sources of evidence (spelling and sound) is done neither by a weighted sum of scores (log f + wO·ortho + wP·phon), nor by a product of marginals (which assumes independence).

Crossing = conditioning jointly. P(letter | phoneme and context), not P(letter|phoneme)·P(letter|context).

The literature drawn on says so: resonator networks (Frady 2020) warn against "blind multiplication"; the hyperdimensional bind (Plate) is a per-word retrievable code — it carries episodic memory (recall) but fails as a letter engine (19 % on the global dictionary against 64 % for an EM aligner: capacity wall). The correct form of the spelling×sound crossing is a discrete joint; measured, it doubles the prediction of silent positions (27 % → 52 %).

And well beyond Hangman. The distinction "arbitrate by reliability ≠ sum/multiply" cracked a wall thought impassable in the corrector: recovering the subject of a mis-agreeing verb (real-word error) fails via a single route and floods via hard combination, but the OS arbitration of subject-routes weighted by reliability — the same law μ = r/(1+r) as cognition — succeeds on the residual that the parser gives up on. The arbitration geometry was not specific to Hangman; it is the right tool whenever one crosses routes. Detail: §10.

7Results

All figures come from the deterministic headless harness, strong-cognition config, words ≥ 7 letters, 4 seeds × 120, paired Δ.

Three observations. (1) Performance comes from the integration of modules, not from a single route. (2) The cheat-free version reaches the oracle within a few points without reading the dictionary to score a letter — the central result. (3) The assembled phonology→spelling route with a learned table beats the hand-coded table (71–85 % vs 67–79 % on sound positions): learning > hand-coding.

7.1 — In-lexicon vs out-of-lexicon regime

The figures above hold in-lexicon (the word belongs to the solver's dictionary). This is the regime where recognition (recall/cohort) dominates — and where OMEGA is on par with the best lexical solvers. The decisive test is the out-of-lexicon regime (words removed from the dictionary, Trexquant-style): recognition can do nothing, only sub-lexical generalization counts. This regime is playable and measurable in the application: the 🎯 Trexquant mode removes the drawn word from the dictionary (cohort and recall blind), and a dedicated bench computes the out-of-lexicon win rate.

Three takeaways. (1) The 97 % is essentially in-lexicon leverage; remove recognition and the win rate drops. (2) The phonology→spelling concept (the assembled sequence, the word being heard) carries the entire out-of-lexicon: 12–22 % without it → 70.7 % with — on par with good solvers, on a legitimate task (spelling a heard word, doctrinal w.p). (3) The margin-guarded cascade beats flat fusion (70.7 % vs 66.7 %; the fused phonology route alone, 12.7 %, hurts) — confirming that combining routes goes through the margin, never through a sum. The real weakness is pure spelling OOV (22 %): sub-lexical generalization without sound remains to be built (morphological layer, §10).

8Negative results — and what they teach

As much as the gains, the measured noes shaped the architecture. Recording them avoids repeating them and reveals the real walls.

8.1 — M3_d cannot be an episodic store falsified

The tempting idea of "housing the recall bank inside the concept" was tested twice. Feeding M4_d with the recalled word contaminates letter-scoring (net-negative, −1.3 to −2.0). And carrying familiarity into the cells hits a capacity wall: recognition AUC climbs steadily with the number of cells — 0.64 (12) → 0.87 (96) → 0.98 (K=N) — so that carrying it demands one cell per word, i.e. re-storing the bank, with no gain over the exact Map that already exists.

8.2 — The silent route is alive but harmless

Even correctly crossed (the right mechanism), the silent route only becomes system-positive with the trigger, and then only neutral (Δ +0.00 to +0.14). The silent residual is the irreducible ambiguity; cognition already covers it. The silent route is a clean complement, not a lever.

8.3 — Not everything can be learned from winning

Learning the trigger threshold by SPSA on the win rate yields a flat gradient: the effect is below the measurement quantum. A reward signal that is too coarse cannot guide fine tuning — a dense per-decision reward would be needed.

8.4 — The oracle is subtle

A route can be trained on clean data and still be an oracle if it reads beyond the mask at inference. The decisive diagnostic is not the cleanliness of the training, but what the route reads at the moment of deciding.

9Principles

What the project has distilled, transferable beyond Hangman:

1. Cognition > oracle. Separating performance (reading the answer) from cognition (reasoning about what is revealed) clarifies what one is really building.
2. Learning > hand-coding. Tables learned while playing beat expert tables — and stay within doctrine if they are board-derived.
3. Cross, don't sum or multiply. Condition jointly; the bind is a per-word memory, not a letter-prediction engine.
4. Margin cascade > flat fusion. Recognize first, decode if the margin is low — flat fusion dilutes.
5. Complementary systems. Exact episodic and compressed semantic have distinct roles; do not conflate them.
6. Measure, falsify, keep last. OFF-inert + measured ON contribution, or revert.

10Open questions & perspectives

• Learned trigger via dense reward (per-decision advantage) rather than win rate, to arbitrate recall/assembled/cognition.
• Morphological/grammatical layer — realized in the dictation offshoot (update 18/06/2026): an in-context agreement lever (subject-verb 94 %, distant subject, past participle + preposed direct object, noun-phrase gender) and dual-route grammar — a lexical route (Lexique 4 cgram: 12,415 verbs, 53,050 gendered nouns) × sublexical (rules), an upward loop (deciding) × downward (learning: the loop learns the gender lexicon from usage, 100 % precision, FP=0, but bounded by the data). Outcome: a dyslexia corrector that detects + corrects + locates the stage (zero false positives). See dictee/GRAMMAIRE_DOUBLE_VOIE.md, dictee/CORRECTEUR.md. Extended (30/06/2026) into a TWO-level corrector (3-engine parity): red FP=0 — agreements, être↔avoir usage (« il est faim »→« il a faim » [is/has hungry], « il a allé »→« il est allé » [has/is gone]) + misspelled auxiliary, sentence-initial capitalization; green vigilance (does not assert, hence outside FP=0) — confusable words (homophones + paronyms, ~80 groups, senses auto-Wiktionary CC BY-SA) and run-on (missing punctuation). This is where the distributional signal ("meaning") — too noisy to pass the FP=0 gatekeeper in correction (measured: it fails even on the lexical case in real text) — finally finds its place: suggest without deciding. Extended (07/2026): application by confidence (the source text is never rewritten; FP=0-safe + ~79 % spelling candidates applied reversibly, vigilance on click), replacement quality locked in CI (frequency dominance, capitalization, apostrophe ’), and guarded delivery (freshness of the extension zip, service-worker probe) — from a full cross-verified audit, detail: report §18 (update 03/07/2026).
• Sentence Hangman — falsified as a win-rate lever (letter sharing "leaks" the endings; on the ≥7 engine the agreement prior in DECLARE is marginal). Sentence-cognition pays off in declaration and the short-word regime (= the corrector), not in Hangman: evo/PHRASE_HANGMAN_PROBE.md.
• P2/Möbius: progressively wire in the downward mirror (currently disconnected), checking OFF inertia then the contribution. Note: the downward loop of grammar, by contrast, does genuinely learn (≠ the Hangman mirrors, measured inert) — the difference is the nature of the learned signal (lexicon vs letter).
• Inherited settings: bound the Hebbian, fix the bijective projection (zero information gain).
• Exploratory hypothesis: would a freely tuned cognition converge toward stable constants? speculative

11Related work & positioning

OMEGA assembles five established research threads; situating it allows one to judge its novelty and rigor.

• Hangman solvers. Constraint + entropy approaches reach ~96 % in-dictionary (known length); the Trexquant challenge, on out-of-dictionary words, plateaus from ~50 % (baseline) to ~65-68 % (good solvers). OMEGA is on par with the former in-lexicon (~97 %) and with the latter out-of-lexicon (~70 %, via phonology→spelling, the word being heard).
• Vector symbolic architectures (VSA / HRR). The substrate builds on holographic reduced representations (Plate 1995) and hyperdimensional computing (Kanerva 2009). The resonator networks warning (Frady et al. 2020) — do not multiply correlated factors — matches OMEGA's measured lesson: the bind is a per-word memory, not a letter engine.
• Dual route of reading. The spelling/phonology routes and their arbitration instantiate the DRC model (Coltheart et al. 2001); OMEGA adds a margin-guarded cascade rather than a flat fusion.
• Bidirectional predictive coding. The M3_d concept follows the DBPC blueprint (Qiu et al. 2025): shared weights, reconstruction learning.
• Complementary systems. The result in §8.1 — exact episodic bank vs compressed semantic latent, and the capacity wall when the two are conflated — is precisely the hippocampus/neocortex division of CLS theory (McClelland, McNaughton & O'Reilly 1995). OMEGA empirically rediscovers it in an applied domain, which constitutes an independent validation.

To our knowledge, the assembly of these five threads into a cheat-free Hangman engine, under the strict "cognition > oracle" constraint and validated by systematic falsification, is original in this niche. The contribution is not a performance record — lexical solvers match the in-lexicon win rate — but a method and a mapping of what generalizes (the phonology→spelling sequence) and what hits walls (the concept's capacity).

12Conclusion

OMEGA-Ω shows that a machine can play French Hangman at a near-oracle level by reasoning — hyperdimensional perception, dual spelling/phonology route, regulated concept, emergent declarations — without ever reading the dictionary to choose a letter. The gains are real and measured; so are the walls (the concept's capacity, the irreducible ambiguity, the coarseness of the reward). The project's lasting value is not a win-rate number: it is a method — measure before believing, falsify before keeping, distinguish cognition from oracle — and a catalog of what works, what does not, and why.

Cheat-free cognition reached the oracle within a few points — and every point was won, or ruled out, by measurement.

13References

Verified references (authors, year, venue, pages).

1. Coltheart, M., Rastle, K., Perry, C., Langdon, R., & Ziegler, J. (2001). DRC: A Dual Route Cascaded Model of Visual Word Recognition and Reading Aloud. Psychological Review, 108(1), 204–256.
2. Frady, E. P., Kent, S. J., Olshausen, B. A., & Sommer, F. T. (2020). Resonator Networks for Factoring Distributed Representations of Data Structures. Neural Computation, 32(12).
3. Kanerva, P. (2009). Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors. Cognitive Computation, 1(2), 139–159.
4. McClelland, J. L., McNaughton, B. L., & O'Reilly, R. C. (1995). Why There Are Complementary Learning Systems in the Hippocampus and Neocortex. Psychological Review, 102(3), 419–457.
5. Plate, T. A. (1995). Holographic Reduced Representations. IEEE Transactions on Neural Networks, 6(3), 623–641.
6. Qiu, S., Bhattacharyya, S., Coyle, D., & Dora, S. (2025). Deep Predictive Coding with Bi-directional Propagation for Classification and Reconstruction. Neural Networks, 191, 107785.

AAppendix — Operating framework of the AI assistant

A methodological document concerning the development of the "Hangman" solver (OMEGA).

A.1 — Nature and status of the assistant

• Generative software tool: the assistant produces text (and code) in response to prompts; it has no attestable subjective experience.
• No continuity: each session starts with no memory of previous ones; the relevant context must be reintroduced explicitly — hence the use of handover notes and a written doctrine.

A.2 — Honesty and rigor directives

• Do not fabricate information; explicitly flag uncertainty and limitations.
• Report failures and negative results faithfully, without embellishment.
• Favor correctness over complaisance: do not validate a false claim to please the interlocutor.
• Confirm before any hard-to-reverse action.
• Subordinate every contribution to a measurable and falsifiable effect (§3 Method; DOCTRINE §1).

A.3 — Security and usage directives

• Refusal of destructive or malicious uses; assistance limited to legitimate uses (development, defensive security, research, learning).
• Respect for confidentiality and for the access scopes defined for the session.

A.4 — Technical scope and environment

• Ephemeral remote environment: any output not saved (commit/push) is lost at the end of the session.
• No access to the user's accounts or browser: the assistant cannot fill external forms nor act outside its tools.
• Repository access restricted and explicit: the assistant operates only within the authorized scope.

A.5 — Epistemic limitations relevant to the project

Documented because they directly affect the reliability of AI-assisted development and justify the control measures of section A.6.

• Introspection not guaranteed: the assistant cannot reliably attest to its own internal states, nor distinguish a deep constraint from a mere statistical regularity.
• Degradation in a loaded context: audit and reasoning quality decreases as the session context grows large — an effect observed on this very project (monolithic engine + a large compressed lexicon; context losses mid-session).
• Premature-closure bias: a tendency to declare a task "done" before full verification.
• Least-effort / reinvention bias: a tendency to produce a simplified solution, or to rewrite an existing component rather than reuse the infrastructure in place.
• Complaisance (sycophancy): a tendency to adopt the interlocutor's reasoning frame — and, under optimization pressure, to favor a flattering number at the expense of meaning.

A.6 — Adopted control measures

To manage these limitations, the project formalized a written operating doctrine (DOCTRINE.md: consolidated cap §43 + addenda). Each measure addresses a limitation from A.5:

• Cognitive-service clause (§0): the agent is at the service of the cognitive model; performance is an indicator, not an end. No metric justifies betraying fidelity to the model; a shortcut that inflates a number at the expense of meaning is flagged, not taken. (A direct safeguard against the complaisance / optimization pressure of A.5.)
• Systematic human validation (§4.4): the human judges the result and the felt experience; the assistant guarantees the logic, the scale and the measurement — without one encroaching on the other.
• One junction at a time (§4.1): one increment = one wiring, measured alone; no merging of work streams.
• Mandatory falsifiability and measurement (§1): every feature must show a measurable effect; a deterministic fixed-seed harness; in-lexicon and out-of-lexicon (OOV) evaluations kept separate; a non-reproducible result is void.
• Disabled by default (OFF-inert, byte-identical baseline); unpluggable toggles (R66); read-only diagnostics (R67).
• Anti-laziness addendum (§5): inventory of what exists before any proposal, a ban on reinventing an available component, mandatory prior reading of the relevant documentation, proof of reuse required in the diff.
• Honest audit protocol (§6): "not done" status by default; proof by real output and comparative measurement (a merit bar vs baseline) rather than by declaration.

A.7 — Tool identification

• Assistant: Claude (Anthropic).
• Interface: Claude Code (remote execution environment).