Daisy chain monitoring layers, Glossolalia/Vickrey table analysis, metacognitive monitoring, void attention, chain convergence proofs.
daisy_chainAnalyze Daisy Chain of monitoring layers with geometric convergence
glossolalia_engineVickrey Table sparse logit lookup analysis for agent inference
metacognitive_monitorStack metacognitive monitoring layers with detection rates
void_attentionAttend to what was NOT chosen -- void attention distribution
chain_convergenceProve geometric convergence rate of metacognitive chain
five_bulesCompute a Five Bules personality profile. The five words -- Try (Fork), Choose (Race), Commit (Fold), Let Go (Vent), Learn (Interfere) -- each measure distance from phi along one axis. A spike indicat...
void_gain_indexCompute the Void Gain Index (VGI). VGI = (K_perceived - 1) / (K_actual - 1). When VGI = 1.0, the walker matches the terrain. When VGI > 1.0, the brain tracks phantom forks (rumination, anxiety). When ...
ocean_comparisonCompare the Five-Bule personality model with OCEAN (Big Five). Partial overlap, not equivalence. Openness loads on Try+Learn (2 primitives). Conscientiousness loads on Commit+Choose (2 primitives). Ne...
system_observationRun metacognitive observation across all daemon void boundaries. Returns C0-C3 scores, daemon health map, cross-daemon correlations, convergence ratio, and actionable alerts. C0=generation health, C1=...
daemon_health_checkCheck health of a single daemon from its rejection history. Returns convergence ratio, dominant rejection dimension, entropy, and dimension count.
resolve_alertGet actionable remediation commands for a metacognitive alert. Returns shell commands that can be executed to investigate or resolve the issue.
thm_daisy_purityThe logit projection W * embedding[t] is a pure function of the token ID. Unlike transformers (where output depends on full attention context), Markov chains have no context dependence. Same token alw...
thm_daisy_linearityMatrix-vector multiplication distributes over the linear state transition: W(α*e[t] + (1-α)*s) = α*(W*e[t]) + (1-α)*(W*s). This means precomputed logits can be interpolated at runtime with zero error....
thm_precomputation_validityThe precomputed Vickrey Table produces exact results. Cached interpolation logits = α * table[t] + (1-α) * prevLogits equals the full matVec logits = W * state, by THM-DAISY-LINEARITY. Zero approximat...
thm_topk_deficitStoring top-K logits per token is a semiotic fold at build time: vocabSize paths collapsed to K paths, deficit = vocabSize - K. The vented logits are nuance paths that don't survive the build-time fol...
thm_absorbing_stateLinear Markov chains with α < 1 converge geometrically to fixed points. After n steps: state = (1-(1-α)^n)*e[t] + (1-α)^n*s₀. For α=0.7: 97.3% convergence in 3 steps. If argmax(W*e[t]) = t, token t is...
thm_glossolalia_completenessThe precomputed Vickrey Table is a complete representation for linear Daisy Chain language models. Any model in this class can be fully captured by its table, with inference on the table producing ide...
thm_identical_trivial_foldWhen all agents in a Daisy Chain MOA have the same α and same projection W, they produce identical logits. The deficit-weighted fold assigns equal weights (1/k). k-1 agents are wasted. This is the for...
thm_diverse_alpha_divergenceAgents with different mixing coefficients α₁ ≠ α₂ produce different hidden states after one step from any non-trivial starting state (s ≠ x). Proof by contradiction via `(α₁ - α₂)(x - s) = 0`. Differe...
thm_moa_cost_with_vickreyThe marginal cost of adding one agent to a Vickrey-backed MOA is V (vocabulary size), independent of hidden dimension d. Without Vickrey: V*d per agent. Savings per agent: V*(d-1). For SmolLM2-360M (d...
thm_moa_deficit_decompositionThe total deficit decomposes additively: Δβ = (k-1) + (V-K). Fold deficit (k-1) is structural (unavoidable). Table deficit (V-K) is a design choice (K is the knob). Minimum: k-1 (full table). Maximum:...
thm_diversity_necessaryFor a MOA fold to extract more information than a single agent, agents must produce different logit distributions. Identical agents contribute zero marginal information. Effective agent count = number...
thm_daisy_chain_moa_designThe design prescription: total deficit is minimized when agents are diverse (different α or W) and the Vickrey Table is maximal (K → V). Full table + diverse agents achieves minimum deficit k-1. Singl...
thm_meta_convergeMetacognitive walker C0-C1-C2-C3 cognitive loop on void surface: eta remains bounded, exploration stays within configured bounds, gait is always a valid cognitive level, inverse Bule measure is non-ne...
thm_five_bule_personalityPersonality is five measurable Bule distances along fork/race/fold/vent/interfere axes. Try=Fork (eta), Choose=Race (temperature), Commit=Fold (commitGain), LetGo=Vent (decayRate), Learn=Interfere (fe...
thm_phi_attractorAll five personality dimensions converge to phi_inv = (1+sqrt(5))/2 - 1. Distance from phi_inv is the Bule (deficit) along each axis [LEDGER: THM-PHI-ATTRACTOR]
thm_bule_spike_detectionA person's pathology is a spike -- one Bule much higher than the others. measureBules() identifies the spike dimension [LEDGER: THM-BULE-SPIKE-DETECTION]
thm_seven_layer_stackRejection propagates through seven personality layers with timescale-appropriate attenuation: mental health 1.5x (amplified), behaviors 0.8x, traits 0.1x, temperament/culture 0.01x [LEDGER: THM-SEVEN-...
thm_ocean_partial_overlapOCEAN (Costa & McCrae 1992) partially overlaps but is not equivalent to Five-Bule. Openness loads on Try+Learn (2 primitives). Conscientiousness loads on Commit+Choose (2 primitives). Neuroticism is a...
thm_personality_weighted_complementPersonality parameters modulate the Buleyean complement distribution: eta controls softmax sharpness, commitGain scales rejection counts, decayRate fades old rejections, feedbackGain scales deviation ...
thm_python_personality_mirrorPython implementation mirrors TypeScript: same five parameters, same derivation, same complement distribution, same stack propagation [LEDGER: THM-PYTHON-PERSONALITY-MIRROR]
thm_frf_positivity0 < K for K >= 1 [LEDGER: THM-FRF-POSITIVITY]
thm_frf_rejection_count1 <= K-1 for K >= 2 [LEDGER: THM-FRF-REJECTION-COUNT]
thm_frf_system_convergesAny ForkRaceFoldSystem converges [LEDGER: THM-FRF-SYSTEM-CONVERGES]
thm_frf_failure_more_infoK-1 > 1 for K >= 3 [LEDGER: THM-FRF-FAILURE-MORE-INFO]
thm_frf_void_growsVoid boundary grows monotonically [LEDGER: THM-FRF-VOID-GROWS]
thm_frf_deficit_decreasesDeficit non-increasing under learning [LEDGER: THM-FRF-DEFICIT-DECREASES]
thm_frf_deficit_convergesDeficit reaches zero or floor [LEDGER: THM-FRF-DEFICIT-CONVERGES]
thm_frf_observer_separationData path strategy != observer strategy [LEDGER: THM-FRF-OBSERVER-SEPARATION]
thm_frf_five_propertiesAny FRF system satisfies all five properties [LEDGER: THM-FRF-FIVE-PROPERTIES]
thm_mindfulness_convergesIterating self-reflection converges [LEDGER: THM-MINDFULNESS-CONVERGES]
From "Being Irreversible" by Taylor William Buley.
LEDGER sections: Daisy Chain, Glossolalia & MOA, Metacognitive Walker & Void Attention
Read the paper at Wallington Lab