AMetric Normal-Form Homology (Black Hole ARC 3)

Overview This manuscript is Paper III of the AASC Black-Hole Endpoint Arc. It proves the AMetric normal-form homology theorem connecting origin-side licensing and endpoint-side exhaustion. The paper preserves the dependency order: kernel→AMetric invariant→licensed physical interior→metric projection→black-hole endpoint exposure\text{kernel} \rightarrow \text{AMetric invariant} \rightarrow \text{licensed physical interior} \rightarrow \text{metric projection} \rightarrow \text{black-hole endpoint exposure}kernel→AMetric invariant→licensed physical interior→metric projection→black-hole endpoint exposure The black-hole endpoint does not authorize AASC. It is classified by AASC. Central Result The paper proves that the origin-side AMetric boundary and endpoint-side New AMetric Boundary are: token-distinct; role-profile identical; structurally homologous; non-transmissively related. The central expression is: BA⋆≠BA0,PANF⁡(BA⋆)=PANF⁡(BA0)=aANFB_A^\star \neq B_A^0, \qquad \operatorname{PANF}(B_A^\star) = \operatorname{PANF}(B_A^0) = \mathsf{aANF}BA⋆=BA0,PANF(BA⋆)=PANF(BA0)=aANF This is equality of complete AMetric role profiles, not identity of tokens. Endpoint Exposure Endpoint exposure occurs only after: exterior quotient subtraction; certificate subtraction; nonempty unresolved residue; undefined old-scope standing transport; residual metric-support exhaustion; false-endpoint route closure; null-route closure. The endpoint is not inferred from ordinary black-hole geometry alone. Exterior parameters, hair-like witnesses, radiation records, boundary maps, leakage channels, reconstruction maps, and richer-scope structures subtract only what they genuinely re-fix. The endpoint proof begins with what remains unresolved. What Homology Does Not Mean AMetric homology does not imply: crossing; inheritance; cyclicity; causal production; energy transfer; information transfer; law transfer; metric continuation; populated successor domain. It is a structural boundary-profile result. No AMetric Fusion The paper includes the no-fusion result for black-hole mergers. Even if exterior Einstein dynamics describes a merger and a single post-merger exterior quotient, AMetric endpoint tokens do not fuse. Co-classification is bookkeeping, not contact, adjacency, or composition. Scope and Nonclaims The paper does not claim to: prove the fresh governed-domain capstone; produce a baby-universe model; assert cyclic cosmology; infer a populated successor; use black holes to derive AASC; treat metric singularities as primitive AMetric boundaries. Role in the Arc This paper exports: New AMetric Boundary exposure; AMetric normal-form homology; no-crossing; no-inheritance; no-fusion under mergers; the boundary-status handoff to the capstone. These results are imported by Paper IV. This paper is downstream of: Non-Degenerate Construction and the Kernel of Admissibility  The Structure of Admissibility