The Exterior Information Boundary of Quantum Black Holes

How much of a quantum black hole can be inferred from measurements performed outside the horizon? We organize the answer as a hierarchy of inverse maps. Existing near-extremal response results show that active, quantum-corrected absorption and transparency data can, within a declared Schwarzian throat model, identify a finite-dimensional effective macrostate. We show that this reconstruction is not quantum-field-state tomography: the isolated black-hole response kernel does not determine a Wightman function, occupation hierarchy, renormalized stress tensor, or full observable-algebra state. For finite exterior experiments, localized Einstein-constraint gluing together with domain-of-dependence uniqueness gives classes of inequivalent completions with identical measured data. For complete exterior information we prove an exact operator-algebraic theorem: if the admissible full theory contains a nontrivial unitary in the full observable algebra that also lies in the commutant of the complete exterior algebra and changes the full state, conjugation by that unitary generates a distinct full state with identical expectation values for every exterior observable at every time. The hypothesis is realized exactly in regulated independent-factor models and, for causally complementary local regions, by microcausality in fixed-background local QFT; microcausality alone does not establish a nontrivial commutant for the complete all-time black-hole exterior algebra. In perturbative gravity, gravitational dressing obstructs exact locality but gravitational splitting supports an order-by-order, charge-preserving approximate analogue; we formulate the corresponding epsilon-indistinguishability bound. In nonperturbative quantum gravity the existence of an independent physical exterior commutant remains theory dependent, and holographic encoding may replace it. The result is therefore an exact theorem for independent-completion algebras satisfying the stated commutant hypothesis, an approximate theorem for perturbatively split gravitational sectors, and a sharp diagnostic dichotomy for exact quantum gravity.