The CoE Invariance Equation for P vs NP: A Coevolutionary Contract for Δ-Stable Transport Under Drift Budgets

This paper proposes a minimal, verifier-first contract that composes two previously introduced components: (i) a registered-window Transport Test methodology for P vs NP, in which reasons are required to travel under admissible perturbations and across audited encodings (e.g., 3-SAT ↔ Sudoku), with progress recorded by a conservative multilayer ledger P(L,t) + NP(L,t) = 1; and (ii) the CoE Invariance Equation, which treats re-encoding as an admissible operator Δ and bounds representational drift via explicit budgets. The contribution is a single Δ-stable acceptance predicate that makes drift-budgeted transport a necessary condition for constructive credit in the ledger. A transported claim is credited to the constructive channel only when an independently verifiable proof-pack artifact exists, the Circle-of-Equivalence (CoE) gate releases, and the evidence signature remains within declared drift budgets across admissible Δ. No claim is made regarding P = NP; instead, the work specifies an auditable contract and a failure taxonomy that localizes brittleness as verification breaks, outcome instability, or drift-budget violations.