A Conditional Proof that P ≠ NP: Reducing the Problem to a Single Rigorous Theorem

We present a self-contained framework that reduces the P̸ = NP problem to a single, well- posed mathematical conjecture: the extension of the rigorous one-step replica symmetry breaking (1RSB) theorem from random regular NAE-SAT to canonical 3-SAT at clause density α ≈ 4.2. All other components of the proof are either rigorously established in the literature (the Overlap Gap Property barrier, the equivalence Franz–Parisi ⇔ Statistical Query lower bounds, exponential mixing for local dynamics) or supported by extensive experimental evidence (universal continuous topological voids, kinetic barriers, and exact scaling relations). We provide a complete technical roadmap that identifies the six existing mathematical tools required for the extension (Poisson cloning, p-biased Fourier analysis, the 1RSB cavity equations, stability criterion, moment method, and the FKCK percolation mapping) and show that, once the extension is proved, P̸ = NP follows logically without additional assumptions