Exact Multi-Arch Lifts of Perturbed Hofstadter Recursions: Residue Criteria, Composition, and Gaussian Profiles (Reproducibility Archive)

This record provides the reproducibility archive accompanying “Exact Multi-Arch Lifts of Perturbed Hofstadter Recursions: Residue Criteria, Composition, and Gaussian Profiles” by Marco Mantovanelli. The paper develops a unified integer-anchor framework for exact residue-class lifts of parity-perturbed Hofstadter recursions, Q(n) = Q(n − Q(n − d)) + Q(n − Q(n − 2d)) + f_d(n). The framework includes the delay pairs (2,4), (4,8), (5,10), (7,14), and (9,18). It gives exact routing and balance conditions, sufficient conditions for positive backward recursion, and minimal prescribed prefixes. Every even delay admits a canonical construction with tailored periodic forcing. The selected odd-delay constructions retain strict alternating forcing. A composition theorem establishes admissible constructions for the multiplicative semigroup generated by 5, 7, and 9; existence for every odd delay remains open. The previously established unit-delay Gaussian profile is used as a precisely identified analytic input. The paper proves its transfer and distinguishes preserved limiting profiles and sharp constants from changing exact zeros, value supports, frequencies, initial blocks, and summatory corrections. A concrete consequence links composition and summation: reversing the order of the five- and seven-delay lifts preserves their leading Gaussian profile but changes their summatory functions by 6N + O(1). The proof identifies common anchors, an exactly periodic difference of period 70, and a period sum of 420. The archive contains the 25-page English preprint, complete LaTeX sources, all five publication figures, Python implementations, original and newly generated numerical arrays, seed files, finite certificates, the exhaustive enumeration printed in the paper, computational audit reports, source provenance, dependency information, and file-integrity manifests. Reported checks include 21,626,880 sequence comparisons, 712,875 exact partial sums, 120,000 complete value multiplicities, and all 25 supplied seed files. Additional composition checks cover 81 pairs of tables and both orders of the delay-thirty-five construction. These finite computations supplement the mathematical proofs. The independent delayed (3,6) word construction remains a separate work and is used only for comparison.