Addendum 4: Guerra–Toninelli Interpolation for the 3‑SAT Spin System

We adapt the Guerra–Toninelli interpolation scheme to the Poisson-cloned 3-SAT model (Addendum 2) with the p-biased Fourier expansion (Addendum 3). We prove a lower bound on the free energy via the stability of the 1RSB solution (Montanari–Parisi–Ricci-Tersenghi 2004) and sketch the upper bound using the variance control of Lemma 5.1 in Addendum 3. Together, the two bounds establish that the free energy of the cloned model converges to the 1RSB prediction, which is the core step in extending the Nam–Sly–Sohn 1RSB proof to canonical 3-SAT.