Horizon Instability as an Admissible Reconstruction Obstruction (Black Hole ARC 1)

Overview This manuscript is Paper I of the AASC Black-Hole Endpoint Arc. It proves the exterior no-totalization theorem for uncertified horizon reconstruction. The paper asks a narrow question: Can an uncertified permanent horizon remain a continuing same-scope standing-preserving exterior reconstruction object? The answer is no. Central Result In a fixed exterior black-hole reconstruction scope, a threatened reference class must be preserved by an admissible exterior route. Acceptable routes include: leakage; evaporation; radiation witnesses; boundary traces; standing-transport certificates; holographic anchor maps; complementarity correspondences; remnant maps; non-sink quotients; declared richer governance. If none of these is supplied, the horizon standing-transport operator remains partial: TH:XH⇀RextT_H : X_H \rightharpoonup R_{\mathrm{ext}}TH:XH⇀Rext and no same-scope totalization is admissible. Exterior-Quotient Subtraction The theorem is stated relative to the declared exterior quotient and witness algebra. All exterior parameters, hair-like witnesses, radiation records, perturbative data, boundary traces, and certificate structures subtract from the threatened burden exactly to the extent that they re-fix standing-bearing content. Whatever remains after that subtraction belongs to the unresolved residue: RHR_HRH The obstruction applies to that residue. What the Theorem Blocks The theorem blocks attempts to treat the following as automatic standing preservation: global retention without exterior recoverability; Page-curve behavior without reference re-fixation; holographic slogans without anchor maps; remnant storage without an exterior remnant map; final-state projection introduced after loss; hidden labels or branch indices; coordinate or metric continuation alone. What the Theorem Allows The theorem does not reject standard black-hole programs. It allows them exactly when they supply the required role: Hawking radiation may be a leakage or witness channel; holography may be a certificate; islands may be a reconstruction-domain certificate; remnants may be admissible if they expose exterior maps; quantum gravity may change scope if its governance is declared. Scope and Nonclaims The paper does not claim to: deny classical event horizons; compute radiation spectra; solve quantum gravity; derive a Page curve; deny global unitarity; classify the final AMetric endpoint; prove the capstone fresh-domain theorem. Role in the Arc This paper exports: standing break; undefined old-scope standing transport; the unresolved residue after exterior quotient subtraction; the no-totalization obstruction. These results feed directly into Paper II’s residual-coherence analysis. This paper is downstream of: Non-Degenerate Construction and the Kernel of Admissibility  The Structure of Admissibility