ESCT v9.8 Mathematical Audit and Roadmap Supplement: Version Genealogy, Conditional Lemmas, Negative Results, AI Boundary, and Level-3 Validation Path

ESCT v9.8 Mathematical Audit and Roadmap Supplement: Version Genealogy, Conditional Lemmas, Negative Results, AI Boundary, and Level-3 Validation Path

ESCT v9.8 數學審計與路線圖補充:版本譜系、條件式引理、負結果、AI 邊界與 Level-3 驗證路徑

This document is a mathematical audit and roadmap supplement to ESCT v9.7b-1, not a mainline version extension. It integrates Claude v9.8 constructive materials, Kimi independent audit reports, Claude-Kimi comparison results, and ChatGPT mathematical correction into a single boundary-controlled synthesis.

The audit preserves two conditional mathematical results: BNMEAT, a centered Bernoulli maximum-entropy lemma that justifies tanh under pulse-coding / binary-support assumptions; and PAAT, a drive-dominant bounded-residual singular-vector alignment theorem with O(1/t) convergence. It rejects rank-only ERCOT as a theorem because independent rank estimates fail to reproduce the observed noise-critical hierarchy. ERCOT is therefore replaced by a dual-mechanism collapse-sensitivity hypothesis involving macroscale Boltzmann attractor suppression and microscale saturation protection.

OP9 is retained as a Level-2 EEG correspondence bridge using A_ref = 20.0 μV/√Hz, but not as Level-3 subject-level empirical validation. AI migration is explicitly bounded: biological ESCT cannot be directly applied to transformer systems, although its collapse-order screening logic may inspire a future independent AI stability assay.

The scientific value of this supplement is not the completion of a first-principles-to-EEG proof chain. Its value is version genealogy, conditional mathematical closure, negative-result documentation, hypothesis replacement, AI boundary control, and a clarified PhysioNet Level-3 validation path.

ESCT; mathematical audit; entropy pressure; maximum entropy; tanh; BNMEAT; PAAT; Wedin perturbation theorem; effective rank; ERCOT; negative result; anesthesia EEG; OP9; PhysioNet; AI migration boundary; theory self-audit; consciousness emergence

Computational neuroscienceTheoretical neuroscienceConsciousness studiesMathematical modelingEEG / anesthesiaAI alignment / AI safety methodology

v1.0. Audit supplement release. This document consolidates ESCT v9.8 mathematical audit results, including conditional lemmas, ERCOT negative result, OP9 Level-2 status, AI migration boundary, and roadmap toward PhysioNet Level-3 validation.

A boundary-controlled mathematical audit of ESCT v9.7b-1 that preserves conditional results, records negative results, and clarifies the remaining empirical validation path.