Multitime Barriers for P vs NP: Why Some Reasons May Not Travel in Polynomial Time

P vs NP is often approached as a question about algorithms and bounds: either exhibit a polynomial-time decider for an NP-complete problem or prove that no such decider exists. This paper proposes a different lens: treat P = NP as a transport property — do “reasons” (the operational structure that makes a solver succeed) travel across polynomial reductions in a way that remains auditable and stable? We frame this through the Temporal State Machine (TSM) kernel of Compositional Clock Theory: decisions occur under multiple clocks (execution, verification, audit), and progress must be governed by admissibility, receipts, and commit depth. We introduce abstain-gated decision kernels under a no-reopen discipline, where the system may refuse to commit unless the evidence is replayable and the recovery budget is feasible. Within this governance-first framing, “transport” becomes a commutation requirement between reductions and receipts: success is not only solving instances, but carrying a verifiable explanation of why the instance is solved that survives encoding changes and can be checked under declared costs. We instantiate the transport test on canonical NP-complete domains (3-SAT and Sudoku, as representatives), not to claim a proof of P = NP, but to define a falsifiable program: either discover a stable, general, receipt-carrying polynomial strategy (supporting P = NP), or demonstrate systematic transport failure that resists any admissible repair (supporting P ≠ NP). The payoff is a structured research agenda that aligns complexity theory with governance and audit, clarifying what would count as credible progress under Clay-level scrutiny.