Entropy-Structured Consciousness Theory (ESCT) v8.1 Abstract ESCT v8.1 addresses five structural weaknesses identified in v8.0 by an independent mathematical review (March 2026). The central fix replaces the hardcoded ignition_boost = 1.5 conditional with a derived continuous suppression model grounded in Mink (1996), making the claimed phase transition genuinely emergent rather than asserted. Four additional fixes eliminate an arithmetic bug in the basal ganglia noise term, make the thalamic half-saturation point derivable from the reference entropy scale, replace an unlabeled magic number in the collapse condition with its literature-sourced parameter, and promote the key signal-detection-theory proportionality assumption from implicit to explicitly labelled (Assumption A4). A DMN/TPN intra-cortical competition stub (L3) is added as a v8.2 scaffold. All v8.0 propositions are retained. 98/98 unit tests pass. Qualia ∉ Domain(C■). Here is the English translation of the analysis: ESCT v7.0 Topology Study: Core Findings Summary 🎯 Methodological Innovation: Topology Filter We implemented a rejection sampling mechanism, strictly enforcing the Pxx heuristic bound within the ESCT framework for the first time: Generate W → Compute ρ = β₁/β₀ → Check ρ ≤ 2·tanh(Π̃) → [Pass/Reject] This ensures simulated network structures possess biological plausibility (similar to real brain's sparse connectivity). 🔬 Key Scientific Discoveries Finding Significance Consciousness stability window extremely narrow Π̃ t_ignition): (1) ρ_AI > ρ_critical (2) d(K_proxy_1)/dt 0.7 ═══ LITERATURE-GROUNDED PARAMETERS (v6.4+) ═══ λ=0.3 (Wendling 2002)γ=1.0 (Friston 2010)σ̄=0.2 (Niedermeyer 2005)G_univ=1.0 (Jaynes 1957)k_sig=6.0 (Wilson & Cowan 1972)α=0.5 (Fries 2005) ═══ CODEBASE ═══ Four-layer architecture: esct_core.py — LITERATURE_DATA, ESCTParams, P16/P17/Pxx (450 lines) esct_sim.py — SimParams, 5 states, ODE solver (295 lines) test_esct_core.py — 62/62 unit tests passed esct_run.py — 4-layer orchestrator, 6 charts, exit 0/1 (376 lines) Run: python esct_run.py ═══ VERSION HISTORY ═══ v1–v4: Five axioms, master equation, Axiom 0 (Π̃), TDAv5–v6: P8–P15, Boltzmann N_attr, bio/AGI proxies, 39 citationsv6.2: P16 Formal Convergence Theoremsv6.3: Perplexity peer-review optimisations, 41 unit testsv6.4: All constants → literature values, Corollary 1: 78%→94%v7.0: P17 criticality_window, Pxx bound, SimParams, 62 unit tests ═══ PERMANENT SPECIFICATION GAP ═══ Qualia ∉ Domain(C_hat(ω,t)) The Hard Problem is not solved — it is precisely bounded. ─────────────────────────────────────Author: Ryan Rong JhouProduction line operator, Yongkang, Tainan, TaiwanNo formal academic affiliationDeveloped in dialogue with Claude (Anthropic), March 2026