Physics as Admissible Potential: Constraint Grammar, Informative Failure, and Basis Integrity

Physics as Admissible Potential reframes physics not as a discipline of prediction, but as a grammar of constraint that specifies what is admissible and what constitutes physical potential. The paper draws a strict distinction between abstract mathematical possibility and physically meaningful potential, arguing that mathematical consistency alone does not confer physical relevance. Within this framework, physics is understood as defining admissibility conditions under which interaction, persistence, and resolution may occur. Once admissibility is established, operant traversal refines admissible potential into probablecontinuation, introducing likelihood as an execution-level consequence rather than a foundational primitive. Prediction is therefore treated as downstream of physics, arising from constraint-weighted traversal rather than from physical law itself. Time and distance are described as derived ledgers of irreversible constraint traversal, not as primitives. Geometry is treated as descriptive of admissibility and closure regimes rather than as generative or causative. Failure is framed as informative boundary information that stabilizes comparison and enables convergence rather than as an error state. The paper further reframes the Millennium Prize Problems as calibrated positive and negative tests of admissible structure. Under this interpretation, classical solvability is secondary to their role in diagnosing basis integrity and boundary conditions. This document is explanatory and non-normative. It does not introduce new physical postulates, mathematical proofs, or falsification criteria. Instead, it provides a disciplined interpretive framework for reading physics, mathematics, and the Unified Resonance Model (URM) consistently. A canonical URM/IP glossary and a plain-English appendix are included to stabilize terminology and accessibility.