Mathine — Evidence In, Trust Out

Multitime barriers for P vs NP: Why some reasons may not travel in polynomial time

Mathine: Multitime Transport Barrier Machine
Link: https://doi.org/10.5281/zenodo.18366941

P vs NP is usually framed as an algorithmic question: find a polynomial-time decider for an NP-complete problem, or prove none can exist. This paper proposes a different lens: treat P = NP as a transport property—do the “reasons” a solver succeeds actually travel across polynomial reductions in a way that remains stable, auditable, and checkable?

The core tool is a multitime governance kernel: decisions happen under multiple clocks (execution, verification, audit), and progress must be governed by admissibility, receipts, and commit depth. Instead of forcing premature closure, the framework introduces abstain-gated kernels under a no-reopen discipline: the system refuses to commit unless the evidence is replayable and the recovery budget is feasible.

Under this framing, “transport” becomes a commutation requirement between reductions and receipts. Solving is not only producing answers; it is carrying a verifiable explanation of why an instance is solved that survives encoding changes and can be checked under declared costs—so success doesn’t evaporate when you move across representations.

The paper then turns this into a falsifiable research program on canonical NP-complete domains (e.g., 3-SAT and Sudoku as representatives): either we discover a stable, general, receipt-carrying polynomial strategy (supporting P = NP), or we find systematic transport failure that resists admissible repair (supporting P ≠ NP). The payoff is a cleaner definition of what “credible progress” should look like under Clay-level scrutiny: not just faster solving, but reasons that actually travel.