Max M. Schlereth

This paper is Part II of a trilogy extending earlier works on the ICB ( e.g. 'AGI is Impossible'(Schlereth, 2025)), expanding upon specific domains of the original proof. Building upon the conceptual diagnosis presented in Part I (“The Canary in the Algorith- mic Coal Mine”), this paper provides the rigorous mathematical proof of the Infinite Choice Barrier. (ICB)1 We demonstrate that the limitations of algorithmic cognition described in the prelude are not merely engineering bottlenecks, but formal inevitabilities derived from a triangulation of three fundamental mathematical domains. Specifically, we prove: (1) via Computability Theory (Rice’s Theorem), that semantic frame adequacy is undecidable from within a system; (2) via Information Theory, that entropy diverges in heavy- tailed decision spaces (α≤1), rendering probabilistic inference structurally unstable; and (3) via Algorithmic Complexity (Chaitin’s Incompleteness), that frame-transcendent insights are algorithmically unrecognizable. Furthermore, weunifytheseresultsthroughacategoricalproofusingSheafTheory, demon- strating that “Gluing Failures” between consistent local semantic sections are mathematically necessary in irreducibly infinite decision spaces. ───────────────────────────────────────────── Stack context (added 2026-05-15): • ICB I — Conceptual diagnosis. Schlereth (2025), PhilPapers ID SCHTIC-15. • ICB II — Formal proof, triangulation, Coq appendix. Schlereth (2025), PhilPapers ID SCHTIC-16. • ICB III — Probabilistic case (P-BOSS, hallucination). Schlereth (2025), PhilPapers ID SCHTIC-17. • ICB IV — CSI architecture, General Cognitive Equation. Schlereth (2026), PhilPapers ID SCHAIN-8. • PTAC v1.0 — Coq machine-verified formalization. Schlereth (2026), Zenodo DOI 10.5281/zenodo.20195456 (GitHub repo: z7xt8zzjb5-prog/PTAC_v.1). ─────────────────────────────────────────────