The Coherence Wall Repaired: Claim Calibration, Mathematical Requirements, and a Conditional Finite-State Divergence Theorem for Kernel-Free Optimizers

This paper supersedes the author’s 2025 Coherence Wall paper, “AGI Architectures Must Mathematically Diverge” (PhilArchive ID: MARTCW-8). It withdraws the unconditional universal modal claim while preserving a conditional result: divergence pressure arises when kernel-free optimizers are required to satisfy heterogeneous, evaluator-indexed requirements without a fixed non-indexical objective and without meeting the stated mathematical requirements. The paper formalizes the indexical/non-indexical distinction, states requirements R1–R5 for any future unconditional theorem, presents a conditional finite-state divergence theorem, and provides a verification protocol, ablation requirements, falsification conditions, and reproducibility materials.