A General Theory of Decisive Experiments

This paper develops a contract-relative framework for decisive experiments: experiments intended not merely to reduce uncertainty, but to authorize a protected scientific conclusion under declared nuisance, safety, reset, resource, provenance, and decision semantics. The primitive state is a configuration consisting of authoritative history and current resource state. A declared authority contract specifies the legal policy language and a typed consequence space, leading to an authority–Nerode equivalence: two configurations are equivalent when every legal continuation has the same protected consequence. The framework separates four distinct questions: language-level target knowability, existence of an executable decisive policy, robust separation after model discrepancy, and finite-budget statistical authority. Exact counterexamples show that set-theoretic factorization need not imply measurable or effective decision; complete ideal-law signatures need not imply finite-horizon learnability; structural distinction need not imply positive robust margin; and distinct laws need not permit finite-shot zero-error discrimination. The paper also gives an I1–I7 impossibility taxonomy and an R0–R5 representation ladder so that failures are typed rather than collapsed into a single “impossible” verdict. The principal technical corridor is a nonlinear mechanism family admitting an exact finite observation-space immersion with persistent episode-level nuisance. In this corridor, active family equivalence reduces to equality of finite experiment-indexed semialgebraic behaviour fibres; a covector filtration stabilizes after at most n−1 steps; exact family equivalence is decidable in principle by real quantifier elimination; and inequivalence yields a finite executable separating suite with an a priori word-depth bound. A halting reduction establishes that no universal exact compiler can decide finite-horizon release for unrestricted effective contextual processes. A worked safety-gated spectroscopy example carries the theory through structural release, adaptive legality, support overlap, finite-risk authority, and an explicit Chernoff calculation.