Technical Addendum to "A Conditional Proof that P ≠ NP": Detailed Proof Plan for the 1RSB Extension

This addendum provides the technical details required to extend the one-step replica symmetry breaking (1RSB) proof of Nam, Sly & Sohn (2021/2024) from random regular NAE-SAT to canonical 3-SAT at clause density α = 4.2. It pinpoints the precise points in the existing proof where the symmetry of NAE-SAT is exploited, shows how to replace the uniform Fourier analysis with p-biased Fourier analysis, sketches the Guerra–Toninelli interpolation adapted to 3-SAT hypergraphs, and outlines the FKCK percolation mapping that yields a persistent second Betti number β2 > 0. The chain of lemmas constituting the final proof is stated explicitly.