P = NP by Exclusion of the SAT Separator Endpoint

This manuscript proves P = NP by excluding the SAT separator endpoint on the unrestricted finite CNF-SAT carrier. The proof is AASC-owned: AASC supplies the endpoint-rigidity argument that excludes the bare negative branch, while Cook–Levin/Karp supplies only the standard endpoint correspondence from polynomial-time CNF-SAT to P = NP. The positive raw branch is Posraw := CnfSATInPolyTime, asserting deterministic polynomial-time decidability of arbitrary finite CNF-SAT. The bare negative branch Sepbare is the raw complement of Posraw on the same carrier. The proof is kernel-first. Theorem-bearing endpoint use is treated as governed construction, and governed construction is possible only under the kernel of admissibility, standing, reference, and irreversibility. The downstream AASC machinery is therefore not an external classifier or a source of theorem standing; it is the fixed-domain consequence layer forced by kernel necessity. Ordinary theoremhood, positive or negative, is kernel-internal when it is genuine theoremhood rather than raw trace. The decisive step is the SAT-local endpoint asymmetry. The positive branch directly occupies the constructive endpoint carrier. The raw negative branch, by contrast, is transported by the SAT lower-bound/no-positive equivalence into the SAT image-separator branch. That branch induces an independent same-domain endpoint-status discriminator on the fixed CNF-SAT carrier. Kernel-forced structural rigidity excludes such discriminators. Hence the SAT separator route is unavailable. It follows that Sepbare is excluded. By raw complementarity, Sepbare ↔ ¬Posraw, the positive branch follows. Therefore arbitrary finite CNF-SAT is decidable in deterministic polynomial time. The final passage from CnfSATInPolyTime to P = NP is the standard Cook–Levin/Karp endpoint correspondence. The proof of branch exclusion is AASC-internal; external complexity theory is used only to identify the official endpoint consequence.