Polynomial Constellations in Deep Arithmetic Space: Data, Code, and Figures for Q(n) = n⁴⁷ − (n−1)⁴⁷ Prime k-Tuple Analysis

Companion repository for the paper "Polynomial Constellations in Deep Arithmetic Space: Empirical Analysis of Prime k-Tuples and the Bateman–Horn Heuristic for Q (n) = n⁴⁷ − (n−1) ⁴⁷. " We searched Q (n) = n⁴⁷ − (n−1) ⁴⁷ over n ≤ 2 × 10⁹, accumulating 17, 908, 247 strong probable primes (25-round Miller–Rabin) with up to 430 decimal digits. The dataset includes: • A proven Structural Exclusion Theorem: (Q (n), Q (n) +2) can never both be prime, since Q (n) ≡ 1 (mod 3) for all n ≥ 2. • 170, 346 consecutive pairs, 1, 691 triples, and 14 quadruplets — instances where four consecutive integers all generate probable primes exceeding 10⁴⁰⁰. • Bateman–Horn consistency: the correction factor CQ = 8. 7 ± 0. 1 yields predictions within 2% of the observed prime count. This repository contains the paper (LaTeX source and compiled PDF), all six figures, data files (quadruplet coordinates and density statistics), and Python verification scripts for independent reproducibility.