AMetric Normal-Form Homology (Black-Hole ARC Paper 3)

This paper proves an AASC-internal theorem of AMetric normal-form homology. The dependency order is fixed and one-way: the AASC kernel forces the admissibility-bearing roles of admissibility, standing, reference, and irreversibility; the AMetric invariant fixes the boundary normal form; standing-bearing physical interiors, metricity, Einstein dynamics, initial data, horizons, and black-hole reconstruction are licensed only downstream. No metric-interior object, equation, singularity, horizon, or endpoint authorizes the kernel or the AMetric invariant. AASC is used here as a constraint formalism. Its operational work is boundary exhaustion and impossibility, not the proposal of a successor cosmology, endpoint mechanism, or preferred continuation law. Once the kernel, AMetric invariant, origin-side licensing profile, and endpointside exhaustion target are fixed, every standing-relevant same-scope alternative must appear in the declared role-profile coordinates, resolve through a certified exterior witness, enter independently governed richer scope, or fail under route closure. At the origin side, the AMetric profile excludes primitive metric, temporal, causal, probabilistic, selector, operator, and inherited-law authority. What ordinary physics calls an initial condition therefore enters only after admission, as a declared anchor, quotient-level tensor, or transition certificate inside a licensed continuation package. Cauchy data, low-entropy cosmological constraints, scalar-field starting values, vacuum choices, and Past-Hypothesis-style conditions may be physically indispensable without becoming primitive sources of their own standing. The admitted interior may then support a faithful four-dimensional Lorentzian projection of the AASC gravity role. In the declared minimal first-response same-scope class, its governed metric/source equation is Gμν + Λgμν = κTclosed μν . This Einstein projection is licensed and bounded. It provides the continuation envelope in which ordinary relativistic initial-value practice, source closure, clocks, records, and causal description have standing; it does not acquire authority over the boundary conditions that licensed it. The endpoint profile is derived clause by clause from downstream role-support exhaustion. When the old-scope metric, temporal, causal, source-ledger, and operator roles no longer have standingbearing support, and no independent re-governance, repair, selector, transport, storage, dynamicaltransition, inherited-law, or admitted-null route remains, the endpoint has the independently fixed AMetric boundary role profile. The black-hole residue theorem supplies the target-class exact physical instantiation. For a certified AASC black-hole target, once exterior-quotient and exteriorwitness subtraction leave a nonempty unresolved horizon-isolated residue, old-scope standing transport is undefined, residual metric successor support is empty, no independent re-governance precedes exhaustion, and admitted nullity is closed, the endpoint is the New AMetric Boundary. Hair-like, dynamical, or richer metric structure avoids endpoint activation only to the extent that it genuinely re-fixes standing before the residue is formed or declares a new governance scope before exhaustion; no third old-scope terminal profile remains. The homology capstone result is B⋆A ̸= B0A , PANF(B⋆A ) = PANF(B0A ) = aANF, B⋆A ∼=ANF B0A . The profiles are token-distinct and role-profile identical. Their homology is structural rather than temporal, and classificatory rather than transmissive. T