The Infinite Choice Barrier I - A Mathematical Canary in the Algorithmic Coal Mine

This paper is Part I of a trilogy that restates and further develops the comprehensive work on the ICB ( 'The Infinite Choice Barrier: A Structural Limit of Algorithmic Cognition' , AGI is Impossible Here is The Proof" (Schlereth, 2025)) , which separates the philosophical from the mathematical view, while expanding upon specific domains of the original proof. We show that while algorithms can perfectly infer within a closed frame (“Inference”), they are structurally blind to step out of it Using the transition from Newtonian to Einsteinian physics as an existence proof, we demonstrate that semantic innovation requires a primitive that invalidates the system’s own evaluation metric–a move no algorithm can execute without external intervention. The barrier is not empirical, but topological: an algorithmic map cannot act as the territory. We conclude that the future of intelligence can impossibly be the automation of judgment (AGI). The wall that this endeavor would have to take is iterally infinitely high (and wide), and invisible on top of that. However, there probably is a way to work with this restraint, but only when truly understanding what this barrier is. The ICB Theorem tries to deliver exactly that. ───────────────────────────────────────────── Stack context (added 2026-05-15): • ICB I (this paper)— 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). ─────────────────────────────────────────────