Non-Backtracking Walks on Digit-Generated Graphs: Contact Spectra, Exact Trace Laws, and the Radius of Normalized Ihara Zeta Limits

This preprint develops exact trace laws for non-backtracking walks on digit-generated graphs, including the Factory graph and cell graphs of the Sierpiński carpet and Menger sponge. A common finite contact state space controls closed-walk counts of every length with logarithmic onset. Under the stated persistence hypotheses, normalized Ihara zeta functions converge on the disc determined by the limiting non-backtracking spectral radius. The manuscript also proves uniform-growth and percolation bounds and convergence of optimal local-pattern supersolution certificates; it does not assert convergence of a prescribed numerical iteration. Classical cogrowth results are identified explicitly. The v1.0 public package includes the current manuscript and source, current alpha v1.0 proof companion, reproduction code, frozen numerical references, integer weights, lower witnesses, exact replay reports and literature records. The historical method audit remains pinned to Part IX v1.1. Detailed postal addresses and obsolete private manuscript copies are excluded. Release: Version 1.0, 15 October 2026; 29 pages, 41 references. This is a new, independent preprint record. The PDF and complete source/reproduction ZIP are supplied. The alpha proof companion is the current public 33-page v1.0 edition, identified by SHA-256 in the archive. Verification scope: public-package replay accepted all 15 stored lower witnesses and 24 integer upper certificates, covering 2,095,170 contexts and 5,993,692 labelled closure incidences. The contact audit checked all 95,148 declared operator entries and 30 readouts with 4,222 rational rows. All 36 selected mutations and 42 optimization-mode entrypoints were rejected. Code, contracts, reference data, integer weights and stored witnesses were preserved. The previous full numerical discovery campaign is retained history, not a new rerun for public packaging. Finite certificate replay does not replace the all-level mathematical proofs or certify arbitrary software inputs. Historical proof-method dependency: https://doi.org/10.5281/zenodo.23340664 (Part IX v1.1). AI assistance and author responsibility: GPT and Claude models were used substantively in proof development, code, numerical computation, literature checking, manuscript drafting and revision. Bin Seol directed the research and experiments, managed the data and evolving definitions, and selected, reviewed and revised the final claims. He is the sole human author and takes responsibility for accuracy, integrity, source attribution and originality. Computational checks are distinguished from mathematical proofs. Related records: the public alpha v1.0 proof companion is https://doi.org/10.5281/zenodo.23384789. The related updated methodological note is https://doi.org/10.5281/zenodo.23384719 (Part IX v1.2). These related records do not change the historical v1.1 audit pin identified above.