Exact non-backtracking trace laws and Ihara zeta limits for digit-generated graphs

Revised preprint release, Zenodo version 1.01 (16 October 2026). This is a new version of https://doi.org/10.5281/zenodo.23384801. The manuscript is the first Graphs and Combinatorics preparation, labelled journal version 1.0: 41 pages, 5 figures, 9 tables and 38 numbered published references. It is a preprint, not an accepted or peer-reviewed journal publication. The paper derives exact closed non-backtracking walk counts for digit-generated graphs, a finite contact-matrix representation with an explicit integer spectrum and logarithmic onset, and the Taylor radius of a normalized Ihara zeta limit under the stated hypotheses. Growth, percolation and local-pattern certificate results depend on the identified alpha companion preprint; finite computations do not independently prove the general theorems. Changes from the earlier release include an example-first presentation, three-dimensional axial-cross/Menger/full-cube comparisons, extremal examples with sigma equal to 0 and 5, Factory graph stages from a tree to cycles and triangles, and separate explanations of generation n, walk length L and certificate-window size kappa. These are graph and theorem regimes, not a claim of a physical phase transition. Files supplied: the current compiled PDF; its flat XeLaTeX source ZIP; and the S1 reproduction ZIP preserving its directory structure. Compared with the earlier public package, all 21 Source/code files, 2 Source/audit contracts and 296 prior Reproduction files are byte-identical. The pinned companion PDF and 12 table-row TeX files are also unchanged. The revised archive adds the current manuscript and source, explanatory figures, finite-example checks and revision provenance. It does not represent a new run of the full numerical discovery campaign. In particular, the earlier 15 lower-witness and 24 upper-certificate checks are retained history, not a full rerun for this revision. Twelve finite comparative examples were checked for the present revision. Computational replay is distinct from mathematical proof. AI assistance and author responsibility: GPT models (OpenAI) and Claude models (Anthropic) assisted substantively with candidate arguments and proof development, verification methodology, code, numerical computation and data analysis, literature comparison, manuscript drafting and revision. Bin Seol directed the experiments and cross-domain stress tests, managed the records and definitions, and selected and reviewed the claims. He is the sole human author and takes responsibility for accuracy, integrity, attribution and originality. Related records: alpha v1.0 proof companion, https://doi.org/10.5281/zenodo.23384789; historical proof-method audit pinned to Part IX v1.1, https://doi.org/10.5281/zenodo.23340664; related updated methodological note, https://doi.org/10.5281/zenodo.23384719 (Part IX v1.2). The latter does not change the historical audit pin. Public files omit the author's detailed postal address. The release remains licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).