Structural Inevitability: Specification-Side Source Disambiguation for Oracle-Limited Verification

Abstract

This paper isolates an oracle-limited verification regime: verification constrained by the evidence channel available after generation. A budgeted post-hoc verifier observes an output through a feasible check family and the induced observation vector. If a true output and a coherent false output induce the same vector, every verifier restricted to that channel must treat them identically. Problem-Solution Isomorphism / Structural Inevitability (PSI/SI) is developed as a specification-side design principle: before inference, it adds source hierarchy, scope, invariants, admissible and invalid methods, success criteria, and output contracts so the intended semantic class has a margin that survives proxy error. The scale claim is conditional: recovery improves with capability only when that margin is preserved and approximation error decreases.