Reproducibility artifact for "The compression defect of a discrete-sine Galerkin section" (Part I) and "The exact row of the Toeplitz–Cayley model" (Part II)

Abstract

Version 1.3 accompanies version 1.1 of Part II of the series, "The exact row of the Toeplitz–Cayley model: coefficient law, Binet–Laguerre remainder, and certified positivity at finite rank" (https://doi.org/10.5281/zenodo.22285620; concept DOI https://doi.org/10.5281/zenodo.22276540). New in this version: the research checkpoint frontier_v0_57 — the post-publication audit of Part II version 1.0 (blind re-derivation of the theorems by scripts that import no code of the project, every prose number recomputed, and two adversarial blocks: an independent end-to-end reproduction of a certified eigenvalue of Table 4 by a Cauchy-integral route, and the envelope, the budget and the transfer tested on that independent row at N = 625), the certified saturation check of the enveloping theorem in Arb ball arithmetic (N = 300, 625, 5000; K = 1..7: supremum of the ratio, attainment at d = 1, sign, two-sided row sums; the source of every number of the new Remark 3.7), the verbatim reports of six adversarial reviews (two of the revision, two complete re-readings of the notes, two verification passes) and the finding-by-finding review record, the q = 11/4 certificate of Part I replayed at N = 1250, 2500, 5000, and the deposited PDF and LaTeX sources of Part II version 1.1 (https://doi.org/10.5281/zenodo.22285620) and Part I version 1.3 (https://doi.org/10.5281/zenodo.22286746). The earlier versions of the notes, shipped in versions 1.0–1.2 of this archive inside the sealed checkpoints, are not shipped in version 1.3 because their title footnote carried a personal address (PACKAGE_REDACTIONS.md lists them with their hashes); no script, data file or replay report is affected. Replay: sh recovered_work/frontier_v0_57/REPRODUCE.sh /path/to/python [--n5000] (283 s, plus about 5 min with --n5000), or sh REPRODUCE.sh /path/to/python --audit from the top level. The cached exact rows are unchanged: the seven row archives of this record are those of version 1.2. Companion research software and audit archive for the two notes. It contains the scripts, the pinned historical inputs, the pre-computed replay reports, SHA-256 manifests of every file, and the notes themselves with their LaTeX sources. Every table entry, figure and certified enclosure displayed in Part II is produced by a script of this package, and every prose number is traceable to one of its replay reports. Requirements: Python 3.10 or later for Part I and 3.11 or later for Part II (the versions the replays were run on), python-flint 0.9.0 (Arb ball arithmetic), mpmath, numpy 2.x, matplotlib. Full replay of Part I: sh REPRODUCE.sh /path/to/python (a few minutes); of Part II: sh recovered_work/frontier_v0_54/REPRODUCE.sh and sh recovered_work/frontier_v0_55/REPRODUCE.sh (about three hours each on one core). Statements of a definite sign are decided only in ball arithmetic, on the appropriate one-sided endpoint; float64 scripts are labelled as probes and decide nothing. Reference environment: Linux x86-64, Python 3.11, python-flint 0.9.0, mpmath, NumPy 2.4.4, matplotlib; Part I additionally replayed on macOS 15 arm64 (Python 3.14.6) and on Linux x86-64 (Python 3.10.12). The artifact is distinct from the notes and has no direct implication for the Riemann hypothesis. Original code is MIT-licensed; project-authored documentation is CC BY 4.0, as detailed in the licence files inside the archive. Anthropic Claude assisted with preparation; Julien Lange is the sole author and assumes responsibility for the release. Versions 1.0, 1.1 and 1.2 of this archive, which contained those earlier versions of the notes, are withdrawn from the repository by the author on the day of this deposit.