Multi-Arch Solutions of a Delayed Perturbed Hofstadter Q-Recursion: Exact Frequencies and Effective Gaussian Profiles (Reproducibility Archive)

This record provides the reproducibility archive accompanying the preprint "Multi-Arch Solutions of a Delayed Perturbed Hofstadter Q-Recursion: Exact Frequencies and Effective Gaussian Profiles" by Marco Mantovanelli. The paper develops a general family of multi-arch solutions of the delayed parity-perturbed Hofstadter recurrence Q(n) = Q(n - Q(n - 3)) + Q(n - Q(n - 6)) - (-1)^n. By prescribing explicit finite initial blocks, the construction generates globally defined positive odd sequences with arbitrarily many alternating dyadic arches. An odd-length list of nonnegative integers determines their individual widths, allowing both equal-width and unequal-width configurations, including three-, five-, and seven-arch examples. The mathematical foundation is an exact signed binary-word construction involving two complementary word phases and two monotone core sequences. This establishes global existence, the six-step increment law, and a systematic method for determining the shortest prescribed initial blocks. The normalized elementary word heights converge uniformly to the Gaussian isoperimetric profile. The paper establishes an explicit, although nonoptimal, convergence rate of O(k^(-1/19)). For every fixed arch configuration, it derives an explicit dyadic limiting profile, exact transition positions, and a sharp relative-error constant. A refined analysis determines all sufficiently large finite-level zeros, tangencies, and residue-class crossings. Complete natural-block frequency laws are obtained for arbitrary unequal arch widths. Remarkably, all configurations share the same limiting frequency distribution, while their finite multiplicities and sharp fluctuation constants can differ. Reversing the order of the arch widths preserves every natural-block frequency histogram but need not preserve the error profile or the minimal initialization. Exact summation identities yield a quadratic main term, a universal logarithmic correction, and an explicit log-periodic contribution. The leading summatory terms depend only on the total arch width, not on the ordering of the individual arches. Reproducibility materials The archive includes the 36-page preprint, its LaTeX sources, ten publication figures, Python implementations of the direct recurrence and the independent binary-word reconstruction, figure-generation resources, initial-value data, finite arithmetic certificates, and machine-readable verification reports. The documented numerical audits include 63,193,088 sequence-term comparisons, 1,166 complete natural frequency blocks, and 67 complete blocks of zeros and residue-class crossings. The accompanying REPRODUCIBILITY.md describes the computational procedures, parameter ranges, and provenance of the verification results. The finite computations supplement the mathematical proofs and do not replace them. All asymptotic results concern fixed arch configurations. The construction provides a general sufficient family of multi-arch solutions, not a classification of all possible initial-value problems. This archive is associated specifically with the delayed recurrence with delays 3 and 6. It is distinct from the previously published unit-delay Odd-Arch family and its reproducibility archive.