Prime Distribution on the 6N Skeleton: A Factor-Resolved Local Model for the Conditional Density of Twin Primes, with Large-Scale Verification

Exhaustive computation of prime occurrence on the 6N±1 skeleton up to 10^10(all 1.67×10^9 centres scanned; 2.74×10^7 twin pairs identified, shells S1–S10),together with a factor-resolved local model for the conditional density of twinprimes. Conditioning on the factorisation of the centre N, the conditional twindensity is shown to be proportional to E(N) = ∏_{q|N, q>3} (q−1)/(q−3). The modelis derived within the Hardy–Littlewood heuristic, validated factor by factoragainst ~10^8 nodes (observed/predicted = 1.000 ± 0.008 across strata spanning a3.3× enrichment range, selecting it over the naïve ∏ q/(q−2)), and shown toreproduce the squarefree bias reported by Puszkarz (2018, arXiv:1807.00406) towithin −0.2% at the matching 10^10 scale. This deposit contains: the five result tables (S1–S10, complete factorisation),the computation and figure-generation code, the two figures, and the manuscript(LaTeX + PDF). Scope. This is experimental/computational number theory. The model is avalidated Hardy–Littlewood heuristic, not an unconditional theorem; nothing herebears on the infinitude of twin primes. Priority for the underlying phenomenonbelongs to W. Puszkarz (2018); the cumulative twin counts coincide with OEISA007508.