What question did this study set out to answer?

The central question addressed is whether P equals NP, ultimately proving they are not equal.

April 5, 2026Open Access

Separation of P and NP

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This work demonstrates that P does not equal NP by analyzing algorithmic limitations in 3-SAT problems.

The central question addressed is whether P equals NP, ultimately proving they are not equal.
Proof by contradiction assuming P = NP
Analysis of polynomial-time algorithms for random 3-SAT
Identification of two primary obstructions to P = NP
Utilization of the phase-sweep closure theorem and Post's lattice
Incorporation of results from algebra and statistical physics
Contradictory implications identified for the existence of polynomial-time algorithms for 3-SAT
Two main obstructions demonstrated: structural completeness and computational intractability
Gibbs measure analysis shows approximate counting needs exponential time under independent bounds
Every part of the proof rests on established results in computational complexity

Michael Hanners (2025) studied this question.

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