OMEGA·Ω Cognitive Hangman Engine · v2-α0

LEX4 · LOADING INITIALIZING

HANGMAN · GAME STATE

Game —

START GAME

Play

Engine

Measurebenches, θ training, sweeps, exports — for research

θ stepbatchseed β minmaxstepbatch θ online Wcη

MATHEMATICS · SUBSTRATE

State Modules

Direct Circle

M1_d Σ shift(letterVec, p) · LDIM —

M2_d Mexican-hat 4×4 zones —

M3_d 12 concept-cells Hebbian —

M4_d cos·W₁ + freq·W₂ + lex4·W₃ —

M5_d softmax(scores / T) —

Mirror Circle

M5_m reward + wordEntry —

M4_m letterPenalty[26] —

M3_m symmetric anti-Hebbian —

M2_m zonePenalty[16] + cvPattern —

M1_m letterScore · 1 - penalty —

STATISTICS · METRICS

Performance Live

Win Rate

—%

—

Coverage

—%

letters revealed

Games

recent games

Ticks

— t/s

Guesses · game

avg —

OS μ · weight φ

—

route —

OS r · φ/ortho

—

signal ratio

W_eff · blend φ

—

— cand.

Top ortho / φ

— / —

route OFF

θ = (α, β)

—

analytique (1,1)

φ penalty ↓

—

feedback OFF

SUBSTRATE · bPC HEALTH

bPC health · concept cells

‖W‖ avg

—

init 0.65 → learns

‖W‖ max

—

cristallisation ↑

Dominant cells

—

recent window · ~10/12

act max

—

~0.42 · sat si →1

max |cos| inter

—

redundancy ↑

‖W phon‖ avg

—

cross-modal

Activation per bPC cell · 0 → 11

Letter Distribution · A → Z

AMZ

[—]SYSTEM Engine ready

EXPERIMENTAL · L01 ENHANCEMENTS

Toggles Phase A + B2

Engine settings — active out of — — click to open

A1 · Orthography

M2_d cvPattern

A2 · Lexique 4

M4_d 88K words

A3 · Word Lex4

M5_m wordEntry

A4 · Decomp

M4_m C/V boost

A5 · Positional

M2_m C/V mismatch

A6 · OS Arbitrage

M3_m via canal OS

B2 · Möbius

M1_m → M1_d loop

M1_m co-decision (0,1)

mirror → letter-score — default OFF (measured neutral, R66)

φ · Phon Route

M1→M5 phonologique (re-init)

φ · OS v07

combines ortho+phon μ(r)

φ · Crossing p

real phonology SAMPA + W dyn

φ · Pure substratee

ortho 40D indep (re-init)

φ · Feedback ↓

top-down phon feedback (Part B)

🎯 Declare word

declare if conf ≥ (1=certain)

🧠 InfoGain

info gain · W=

IG x P(succes)

weights IG by P(presence) — requires InfoGain ON

bPC M3_d

concept polyvalent (decouple)

Couplage readout

concept-reward -> score (stripped) — weight W: (sweet 0,20)

Couplage readout φ

concept phon -> score — weight W: (parite ortho)

Concept bound φ (step 2)

readout reads the bind code (revealed-aware) vs blend — separate buffer, baseline intact

🎯 Declare BPC

concept M3_d -> declare word — CONF: (sweet 0,95)

🦴 Declare DUAL (cheat-free)

board-buffer · freq×ortho×phon — conf wO wP

🧠 Learn from cognition

anti-crutch · OS θ + mirror + phon ← cognitive letter

θ · Learning

master : autorise Train θ (§6.5)

θ · Guard 1 bounded

0,1 ≤ α,β ≤ 5

θ · Guard 2 audit

alerte si |w−analytique|>0,2

θ · Guard 3 MDL

rappel λ vers (1,1)

θ · Guard 4 coherence

rejects winrate↑ / coherence↓

θ · ONLINE Learning (SPSA)

per game · guards live · §6.3

🦴 Declare emergent · recall

reconnaissance VSA · banc appris en jouant

🧬 Declare emergent · phon→ortho

assembled decoding · generalizes to new word

🔤 g2p appris en jouant (online)

phon→ortho learned from played words · otherwise batch

🧩 Declare NEO · master

recall + assembled + cohort + silent + trigger · cheat-free

🔁 NEO · recall (addressed)

recognizes an experienced word · 100% on repeated

🧬 NEO · assembled (phon→ortho)

sound positions · generalizes to new word

🎯 NEO · cohorte (filtre board)

board-derived · prunes impossible letters

🔊 NEO · board-derived sound (cohort)

cheat-free · true-sound in-lexicon parity · purity guard ≥

🔗 NEO · joint sound×ortho (crossed)

croiser, pas argmax · +2,2 pts vs argmax (K=1) · seuil

🧭 NEO · arbitrage OS (2 voies DRC)

convex blend sublexical⟷lexical · clean alternative to the cascade

🔠 NEO · letter n-gram (pre-computed)

positional stats of the lexicon (≠ learned from the game) · targets true OOV

🔁 NEO · OS-arbitrated n-gram (auto-regime)

sub=n-gram, lex=cohort · auto reliability switch · in-lex≈cohort, OOV≈n-gram (§1.9) · requires OS arbitration ON

🧩 NEO · n-gram gap-aware (C)

plus proche voisin révélé à distance 1..4 · +2 pts OOV, coût in-lex nul (§1.10) · 1er gain cognitif > substrate

🧪 NEO · g2p revealed + penalty

learns from revealed positions only · pen

🔇 NEO · silent (by sound, crossed)

joint phonogram · silent continuation

🎚️ NEO · trigger (cognition incertaine)

engages the silent only if cognition gap low

🎯 Mode Trexquant (hors-lexique)

the played word is removed from the dictionary — OMEGA generalizes (phon→ortho)

Engineering · Smoke · Bench · Channels · Inventory

OMEGA-Ωcognitive architecture of English hangman — “cognition > oracle”

Dual orthography/phonology route (DRC) on a hyperdimensional substratee · emergent cheat-free declaration · measurement & falsification discipline (R66). Details: memoir & reference report.

concept 1024D · lexical 512D ~97.5% cheat-free in-lexicon Lexique 4 · CC BY-SA 4.0 not loaded

§1 Anti-regression smoke tests (Fix-Final §19.9)

// Smoke tests prêts. Cliquer pour valider que v1-α1+R40 charge sans régression.

§2 Bench R1 — Cible ≥ 500 ticks/sec

Tick estim.

—

ticks/sec

—

cosineSim

—

circularShift

—

// Bench prêt. R1 = ticks omegaStep par seconde sur SDIM=1024.

§3 State runtime + MVP channels

// State OMEGA-Ω. Click "initOmegaGlobals" pour démarrer.

// Inspection canaux + inventaire L7.

§4 Day 2-7 plan (stubs present, to implement)

Day 1' ✅ DELIVERED: Refactor blueprint (M1_d LDIM + D1-D5 + stubs) · Jour 2' : M2_d Mexican-hat 4×4 zones (§6.6.4-bis) · Jour 3' : M3_d 12 emergent Hebbian concept-cells (§6.6.4-ter) · Jour 4' : M4_d Lex4 LETTER_FREQ_FR (§6.6.4-quater) · Jour 5' : M5_d softmax adaptatif · Jour 6' : Naming canaux finaux + OS dialectique v1 · Jour 7' : MVP validation direct circle + R40 true final blank · Phase 2 : Mirror circle + pattern+mirror equations.

The stub functions raise a clear NotImplementedError to signal what remains to code.