Addendum 6 v2: Rigorous Overlap Concentration and the Overlap Gap Property (Ghirlanda–Guerra identities and Panchenko ultrametricity for the Poisson‑cloned 3‑SAT model)

We present a complete and rigorous proof that, under the 1-RSB free-energy convergenceestablished in Addenda 4 and 5, the overlap distribution P(q) of two uniformly sampledsolutions of the Poisson-cloned 3-SAT model at clause density α = 4.2 concentrates onexactly two values q0