Randomized trial proves conditional separation of P and NP in a mathematical framework, suggesting broader implications.
Key Points
This research aims to establish a conditional separation between the complexity classes P and NP within the context of the saturated SAT layer framework.
Developed a typed framework called Six Birds Theory to analyze closure formation in mathematical structures.
Defined a saturated SAT layer, T!SAT, which represents polynomial-time SAT computations and their audit data.
Established translation theorems connecting this framework to standard SAT semantics.
Proved SAT ∉ P under specific conditions dictated by the structural hypothesis ΓCSL-SAT-hidden.
Demonstrated that formed-SAT closure implies P ≠ NP when viewed through Ipoly's constructions.
Identified that the canonical lexicographic SAT-branching readout is not a lawful current observable.