Evidence to Entitlement: Uncertainty-Qualified Certification for Context-Typed Descendant Laws

Abstract

This paper asks under what conditions finite evidence licenses a directional claim about a declared context-typed semantic condition. The constitutive question—what a descendant-law candidate must truly satisfy—and the epistemic question—what finite evidence licenses us to say about that satisfaction—are different objects. The present proposal represents finite evidence D by a retained uncertainty set U(D) and evaluates a declared semantic discrepancy g_C against a tolerance ε_C. Directional claims are licensed only when the full retained set lies on one side of the boundary: if the upper semantic envelope U_C(D) is no greater than ε_C, the condition is CERTIFIED_ADEQUATE; if the lower envelope L_C(D) is greater than ε_C, it is CERTIFIED_INADEQUATE; otherwise the correct outcome is REFUSE_UNRESOLVED. Conditional on the realized state lying in the retained set, the two directional certifications are sound. Enlarging retained uncertainty can preserve or destroy a certificate but cannot create one. When the downstream semantic object is not directly available, an upstream certificate does not transfer automatically. A positive license may instead be transported through a prospectively declared typed bridge. The bridge is one-sided: failure of a sufficient upper bound is not evidence of semantic inadequacy. An exact heteroskedastic counterexample shows that perfect mean-response agreement need not control second-order semantics, while linear-Gaussian and observable-kernel constructions provide positive bridge families. Set-valued model uncertainty and repeated-sample calibration are retained rather than collapsed into a favorable model or nominal interval claim. The prospective evidence includes both support and refusal. A real-flight Nano-Drone benchmark supports an external-native adequacy certificate and a separate short-to-long bridge. A second Coupled Electric Drives host supports all six frozen context-depth transfers on its fixed TEST episodes, with the small TEST count kept explicit. NASA and XJTU battery programs are retained as external refusals rather than repaired into a successful third host: the NASA branch fails its TRAIN host/endpoint gate, while the final XJTU raw TRAIN attempt is directionally error-free but fails preregistered informativeness gates, without proceeding to a confirmatory raw-TEST evaluation. No individual uncertainty-set construction, equivalence margin, robust supremum/infimum rule, abstention device, bootstrap interval, or conformal set is claimed as new mathematics. The bounded contribution is a candidate law-level evidence-to-claim architecture that ties retained uncertainty, context-typed semantics, typed transfer, calibration, and first-class refusal to the descendant-law question. It is not a fourth constitutive lawhood condition, a universal confidence theorem, or an algorithm from data to objective lawhood.