BNCT / TASI – Appendix B: Convergence & Alignment Logs

Appendix B: Convergence & Alignment Logs (Supplementary Materials) This archive provides non-normative audit logs documenting how external large language model (LLM) reasoning systems converge—or fail to converge—onto the structural spine of BNCT / TASI (Time-as-Indexing) under constraint-driven probing. The materials contained here do not constitute validation, proof, or empirical support for the theory. Instead, they record observable convergence behavior, attractor transitions, and surface-level deformations in LLM outputs when specific explanatory primitives (e.g., observer, consciousness, collapse postulates) are explicitly banned and finite-capacity, irreversibility-first premises are imposed. Scope and contents B.1 Session-level convergence trace from a temporary Gemini thought-experiment session, capturing attractor transitions (G0–G3) under controlled constraints. B.2 Gemini deep research analysis, including attractor taxonomy, safety-layer deformation diagnosis, and mappings to existing physical interpretations (records theory, relational time, information thermodynamics). B.3 Independent GPT-based audit assessing logical consistency, novelty position, and the role of safety/alignment layers. B.4 A structural alignment audit cross-checking B.1–B.3 against the core claims of BNCT / TASI, explicitly distinguishing points of alignment, conditional convergence, and non-claims. Key observations Across multiple artifacts and analysis layers, a common structural spine is reached only under deliberate constraint: finite capacity → impossibility of perfect recurrence → structural irreversibility → time as an index of irreversible updates, with entropy treated as a downstream footprint rather than a causal origin. However, this convergence is guided rather than spontaneous and exhibits measurable tensions, including attractor oscillations and safety-layer-induced output deformations. Important notes These logs are provided for transparency and reproducibility of analysis, not as theoretical endorsement by the models involved. LLM outputs are treated strictly as observable behavior under context and constraint, not as authoritative statements about physical reality. The primary BNCT / TASI manuscripts remain fully independent of these materials. Intended use Supplementary appendix (Appendix B) accompanying the BNCT / TASI papers, serving as an external reasoning-system audit and convergence record.