The Black Hole Information Paradox - A Category-Error Analysis

We argue that the black hole information paradox is not a physics problem awaiting aquantum-gravity solution. It is a category error that most plausibly arises from semi-classicalframing on both sides of the debate. Quantum information is defined relative to a well-posedHilbert space and a geometric structure that supports it; in a singular regime the geometricstructure undergoes a phase transition severe enough to render the category itself inapplicable.A conservation law cannot be violated in a regime where its definiendum does not obtain.What survives is geometric residue—most plausibly topological invariants of the manifoldstructure—rather than quantum information in the standard sense. No new dynamics areproposed; the contribution is the identification of the category error and the explicit markingof what has and has not been claimed.