Safe Separability for Autonomous Authorization: Branch-Relative Authority Closure Under Decision-Critical Uncertainty

Autonomous agents increasingly act before all authorization-relevant facts are known. The difficult case is not only whether an action is permitted, but whether the agent may legitimately obtain the evidence needed to determine what should be permitted. We formalize this circularity as safe separability: compatible possible worlds may require different authorization decisions while the actions needed to distinguish them are themselves authorization-sensitive. A safe policy must resolve such decision-critical uncertainty using only probes legitimate in every world still compatible with the current branch. We define exact joint-state semantics over knowledge and authority and identify a restricted Monotone Closure-then-Authorized Sensing class in which authority-only actions can be saturated without loss of resolvability. A direct generalization fails: an action that is globally informative may become observation-constant after earlier evidence while remaining necessary for authority progress. This motivates Branch-Relative Authority Closure (BRAC), which recomputes authority closure after each observation relative to the remaining compatible worlds. Across 266 permanent regression tests, exhaustive evaluation of 256 four-world outcome systems, 1,250 randomized certified comparisons, and controlled stress tests with up to 10,000 worlds, BRAC agrees with exact joint-state search within the tested monotone, world-independent model. Minimal counterexamples involving world-dependent grants and revocation expose the limits of the normalization. These results establish a reproducible authorization-specific branch-relative closure framework for safe evidence acquisition under decision-critical uncertainty.