The Identification Quotient: A Boundary Theorem for Generator Identification Under Declared Regimes

This paper formulates an identification quotient for finite deterministic verification regimes. It asks what a bounded verifier can identify about a purported generator when evidence is restricted to a declared admissible regime. The central result is conditional: relative to a declared notion of admissible evidence, generators can be identified exactly up to the basis-presented equivalence class induced by the regime, and no finer distinction is verifiable without changing or extending the regime. The paper separates the ceiling and attainment directions. The ceiling depends on the exclusion of unmediated probes from admissible evidence; attainment depends only on the inclusion of declared-invariant evaluation. This distinction prevents the result from being mistaken for a purely definitional theorem while preserving the paper’s main boundary claim: undeclared side channels are not refutations of the regime, but regime changes. The result sharpens the Gate between constraint and identification. It does not identify a final generator, deny ontology, or claim that within-class distinctions are unreal. It characterizes where finite deterministic verification stops: at the declared quotient. Stronger forms involving indexical access, stochastic evidence, compact-metric regimes, Galois-style closure, and machine-checked finite cases remain open.