PvsNPResolutionStatus
plain-language theorem explainer
PvsNPResolutionStatus records the resolution state for P versus NP inside the Recognition Science complexity assembly. Researchers tracking RS dissolution versus conditional non-naturalness arguments would cite it to monitor Path B completion against the remaining UniformTopologicalObstructionHyp gap. It is realized as a plain structure whose fields are populated directly in the downstream currentStatus definition.
Claim. A status record $S$ with boolean flags for conditional proof availability and dissolution proof, a string field describing any open gap, and a natural number counting remaining sorrys in the derivation chain.
background
The module assembles two routes to resolve P versus NP. Path A conditions on UniformTopologicalObstructionHyp to obtain exponential circuit lower bounds from J-frustration. Path B is the unconditional dissolution route encoded in the sibling PvsNPDissolution structure, whose three fields assert polynomial R̂ recognition time for SAT instances, unit J-cost lower bounds for UNSAT instances, and local blindness under partial decoders. The status structure simply aggregates the truth values of these routes together with an explicit gap description.
proof idea
The declaration is a structure definition. Its fields receive concrete boolean and string values in the one-line wrapper currentStatus, which hard-codes dissolution_proved to true and sorry_count_in_chain to 1 while naming the remaining hypothesis.
why it matters
The structure anchors the P vs NP assembly and is referenced by currentStatus, which reports dissolution proved while leaving the UniformTopologicalObstructionHyp open. It sits inside the broader RS treatment of complexity via J-cost, spectral gap, and circuit lower bounds, closing the unconditional dissolution path while flagging the conditional route that would complete the forcing-chain derivation of D = 3 and the eight-tick octave.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.