The Class-Mismatch Problem: Why Some True Theorems Are Structurally Undiscoverable

This paper introduces a law-level explanation for a persistent epistemic phenomenon: the existence of true statements that remain systematically undiscoverable by certain solvers, even when no syntactic inconsistency, resource bound, or Gödel-type limitation applies.

Working within the Tier–0 (Ω–Δ–∂) framework, the paper shows that incompleteness can arise from kinetic class mismatch between a problem’s intrinsic structural requirements and a solver’s admissible Anchor–Flow dynamics. Solvers are modeled as inducing trajectories in ΦΓ-structured containers, and each solver/world pairing is assigned a measurable kinetic signature. A quantitative mismatch functional (“Γ-friction”) determines whether a solver can survive recursive constraint filtering and deposit stable records.

The main result proves that when Γ-friction exceeds a class-dependent admissibility threshold, solver survival fails prior to record formation. As a consequence, some truths defined as stable invariants of an admissible world, are structurally undiscoverable for entire classes of solvers, regardless of time, memory, oracle access, or syntactic expressivity.

This yields a strict, agent-relative strengthening of classical incompleteness: the obstruction is not logical or computational, but kinetic. The framework explains why some lawful domains appear random, why both human reasoning and AI systems systematically stall on certain problem classes, and why scaling alone does not resolve these failures.

The paper is not a new physical model and does not modify existing theories. It operates at the law-level, providing a unified epistemology grounded in admissible closure, record formation, and solver–world compatibility. Gödel incompleteness, computational complexity, and formal provability remain intact but are shown to be orthogonal to the kinetic obstruction identified here.