Exact Off-Ratio Lifts of Perturbed Hofstadter Recursions: Periodic Forcing, Gaussian Arches, and Rigidity (Reproducibility Archive)

This reproducibility archive accompanies Marco Mantovanelli's preprint "Exact Off-Ratio Lifts of Perturbed Hofstadter Recursions: Periodic Forcing, Gaussian Arches, and Rigidity" The preprint constructs positive integer solutions of the delayed Hofstadter recursion Q(n) = Q(n − Q(n − a)) + Q(n − Q(n − b)) + f(n) with periodic forcing and nonzero Gaussian arch profiles beyond delay ratio 1:2. For every integer p ≥ 2, the odd-arch family P_p admits an exact residue-class lift whenever 1 ≤ a < b, b ≥ 2a, and 3 gcd(a,b) divides b − 2a. Writing d = b − a, the forcing has period dividing 2d, values in {−d, d, 3d}, and mean 2(b − 2a)/3. A residue clock combines the base recurrence with a second exact identity. Explicit finite positive initial blocks ensure strictly backward evaluation. The lifts preserve the established Gaussian profiles and their sharp relative-error constants. Their value support contains all sufficiently large positive odd multiples of d, has density 1/(2d), and has limiting mean multiplicity 4d over attained values. For a fixed clock, the same forcing supports infinitely many distinct solutions with 3, 5, 7, … source Gaussian arches. If the output is eventually equal to P_p, eventually periodic forcing requires the original delay pair {1,2}. In particular, the bounded three-valued forcing retaining P_p at delays (2,3) is not eventually periodic. A linear residue-profile balance supplies further obstructions. The arithmetic criterion classifies the stated clock mechanism; periodic-forcing arch solutions at (1,3) and (2,3) with different outputs remain open. The deposit includes the preprint, complete LaTeX sources, vector figures, an arXiv source package, and a reproducibility archive containing programs, exact numerical data, initial blocks, forcing words, finite certificates, verification reports, and provenance documentation. Seven explicit examples are covered by a complete verifier printed in the manuscript.