PvsNPStructuralCert
plain-language theorem explainer
The structural certificate for P versus NP requires exactly five complexity classes together with a recognition budget fixed at 360 units that factors as eight times forty-five. Researchers working on complexity questions inside Recognition Science cite this to anchor the per-cycle bandwidth to the eight-tick octave. The definition records these three facts directly from the class enumeration and the budget arithmetic.
Claim. A record asserting that the set of complexity classes has cardinality five, that the recognition budget equals 360, and that this budget equals $8 times 45$.
background
The module develops a structural approach to the P versus NP question by counting complexity classes and fixing a per-cycle recognition budget. ComplexityClass enumerates the five classes P, NP, coNP, PSPACE, and EXPTIME. The recognition budget is defined as eight times forty-five, corresponding to the eight-tick octave times gap forty-five.
proof idea
The structure is introduced by declaring its three fields: the cardinality of the complexity classes, the equality of the budget to 360, and the factorization of that budget as eight times forty-five. No further proof steps are required beyond these direct assertions.
why it matters
This structure supplies the certificate that the downstream definition pvsNPStructuralCert instantiates explicitly. It encodes the key numbers from the module: five classes matching the configuration dimension and the 360-unit budget arising from the eight-tick period. The declaration supports the structural lower-bound argument for P versus NP by anchoring the workload threshold to these Recognition Science constants.
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