Safe Separability under Revocable Authority: Destructive Evidence Coupling, Branch-Conditioned Adaptivity, and a Fixed-Parameter Behavioral Kernel

Abstract

Evidence gathering is usually treated as epistemically helpful: each observation reduces uncertainty, and planning decides which observation to obtain next. That intuition breaks when obtaining evidence can also destroy the authority needed to obtain later evidence. We study this coupling in a finite deterministic model of authorization-sensitive information acquisition. A probe both partitions the compatible worlds and updates a set-valued authority state through fixed requirements, grants, and revocations. The objective is not exact world identification, but only enough separation to determine the required decision. We first show a three-world obstruction in which every decision-incompatible pair has an initially legitimate separator, yet no safe resolving policy exists because either first probe revokes authority needed by the unresolved branch. We then derive an acyclic evidence-precedence certificate, show why global acyclicity is not necessary under adaptive branching, and obtain an exact quotient based on unresolved decision obligations and authority tokens relevant to remaining probes. Behaviorally equivalent probes can be dynamically merged, yielding at most Bell(2k)2^(3r) probe types for k unresolved decision obligations and r relevant authority tokens. This gives fixed-parameter tractability in k + r for the stated model. Independent exact solvers, exhaustive slices, 2,500 randomized differential instances, and controlled capability-gate traces support the theory.