P equals NP.

This is the frozen contract wording. Read the YES and NO tests, the evidence requirements and the undecided cases before taking a position.

Canonical title

P equals NP.

Exact hypothesis · technical wording

The uniform complexity classes P and NP over finite binary strings are equal, using deterministic polynomial-time Turing machines and polynomial-time Karp reductions. Runtime is worst-case in input length, not average-case or restricted to physically encountered instances.

Each round reads the evidence that was public at a stated cutoff. Later evidence goes into a later round; the market itself has no expiry date.

Resolution criteria

YES: An unconditional ZFC proof of P = NP, for example a correct polynomial-time algorithm for Boolean satisfiability with a proven worst-case bound. NO: An unconditional ZFC proof of P != NP. Oracle separations, heuristic success, conditional hardness and failure to find an algorithm settle neither side. Independence from ZFC leaves this market UNDECIDED. Reference sources: Clay: P versus NP (https://www.claymath.org/millennium/p-vs-np/). Evidence policy: use public primary research with methods and uncertainty, plus the named reference sources below. A preprint can inform the estimate but cannot alone meet a terminal criterion; require a peer-reviewed primary result and an independent reproduction using non-overlapping observations or independently prepared samples, unless this is a mathematical proof or the specific criterion instead requires independently implemented calculations. Report data provenance, exclusions, calibration, statistical model and systematic uncertainty. Independence means different data acquisition, not two papers reanalysing the same sample. For a quantitative terminal test, both independent results must meet the stated threshold; disagreement or an interval crossing the boundary means UNDECIDED. Use the final corrected version public at the signed round's evidence cutoff (UTC); exclude later evidence until a later eligible round. Every report in a terminal round must use the same cutoff, covered by the verified signed context and enforced by the configured terminal protocol; a different cutoff requires a new eligible round, never reinterpretation of a signed report or mutation of an immutable binding. This market has no calendar expiry. Retracted findings cannot supply a terminal result. If a named source disappears, use its DOI/publisher or an archived identical version, then an equivalent primary publication applying these unchanged definitions; if none is accessible, remain UNDECIDED, never substitute a different test. Missing data, failed replication, a null search outside the specified domain, or an untested alternative is not automatically NO. These are instructions for evidence assessment, not an automatic truth oracle: scientific interpretation and systematic-error judgment remain. Settlement follows the configured platform mode: terminal mode requires one valid round with all three frozen models returning the same explicit YES or NO and criterion_met=true; any UNDECIDED, failure or disagreement leaves it unresolved. Legacy proposal/challenge mode requires its recorded review process. Model agreement does not prove scientific truth. Invalidity is not NO and this text does not authorize a refund or cancellation: only a cancellation rule disclosed before exposure, if the configured contract supports it, can apply. Otherwise pause new entries and preserve holders' existing rights. Never reinterpret terms after listing.

The definition does not change when an AI estimate changes. Read the listing policy and this market's settlement status.