Verification scripts and data for "A Divisor-Weighted Golomb Sequence: Zeta Asymptotics and Arithmetic Fluctuations"

Abstract

This software and data package accompanies Marco Mantovanelli's preprint"A Divisor-Weighted Golomb Sequence: Zeta Asymptotics and ArithmeticFluctuations". It supports the computational study of OEIS A400220,the unique nondecreasing sequence A of positive integers in which each moccurs exactly B(m) = sum_{d|m} A(d) times. The package contains: - A C++17 generator using a divisor sieve and block endpoints, with explicit checks for unsigned 64-bit integer overflow.- Two separately implemented Python verification programs covering literal block expansion, divisor sums, a nested recurrence, Mobius inversion, prime criteria, divisibility inequalities, iteration to a fixed point, and divisor-layer identities.- The first 10,000 terms of A, its multiplicity sequence B, and the block-endpoint sequence F.- Exact triples (A(m), B(m), F(m)) through m = 100,000, JSON verification reports, recorded large-run results, and numerical diagnostics.- Reproduction instructions, tested software versions, and SHA-256 checksums. A bounded reproduction freshly generated 100,000 blocks and checked allinteger triples against the supplied data. The recorded large run covers10,000,000 complete blocks, representing 260,033,782,794 sequence positionsin compressed form. The full large run was not repeated in the boundedreproduction. The exact Python checks require no third-party packages. Optionalhigh-precision numerical diagnostics use mpmath. The accompanyingpreprint contains the mathematical proofs; the finite computationsprovide reproducibility checks and numerical illustrations. AI tools assisted with the manuscript and verification-programdevelopment, as described in the preprint's AI-Disclosure.