P vs NP — Complete Proof Program is a structured, auditable “proof program” that organizes a candidate corridor toward a Clay-style separation claim into explicitly named nodes with formal interfaces, dependencies, and closure obligations. The document emphasizes verification discipline: each critical component is tagged by status (e.g., GREEN/YELLOW), with YELLOW nodes treated as unresolved proof obligations that block any unconditional headline claim. The core technical spine develops a hard-slice construction, a canonicalization/membrane layer intended to preserve boundary expansion under controlled equivalence moves, and a pressure-test/counting framework that yields lower bounds in a restricted windowed proof model; these bounds are then connected to standard proof-complexity statements via explicit simulation bridges. The current release is intended as a research artifact for rigorous review: it separates unconditional consequences from conditional chains, lists non-claims, and provides a roadmap of what must be proved or cited to reach a fully unconditional Clay-target theorem.