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:

1. Non-Degenerate Construction and the Kernel of Admissibility

2.  The Structure of Admissibility