A certified re-check that every cubic bipartite graph on at most 68 vertices has a cycle of length 4, 8 or 16 (not new; a witness-checked recomputation)

We re-check, with exhaustive search and machine-checkable certificates, that every simple cubic bipartite graph on at most 68 vertices contains a cycle of length 4, 8 or 16 (equivalently: no connected linear v3-configuration with v ≤ 34 avoids Berge 4- and 8-cycles). We follow the growth search of Tranquilli (arXiv:2608.02675), whose certified range stops at 58 vertices, in two root modes: triangle-rooted (his mode; for orders 62–68 it needs the literature premise n(3,10) = 70, which we read only through the Exoo–Jajcay cage survey) and arbitrary-root (no triangle assumed, no cage premise). Two oracles for the forbidden-cycle test give identical decision-transcript hashes at every cap. Route 2 (arbitrary root) caps 29–34 and route 1 (triangle-rooted) caps 30–35 close with 0 completions. Certificate streams are accepted by the producer's two checkers and by an independent auditor's own C checker; the 68-vertex arbitrary-root stream was regenerated by the auditor and has the same sha256 (0112b808…fad5). This is NOT a new bound. Ripatti (BAIKAL/MOTOR 2017, one-page abstract) claims, without a certificate, that the smallest cubic graphs without cycles of length 4, 8, 16 have 78 vertices, which covers every cubic graph on at most 76 vertices, and Ducoffe–Dumitru (arXiv:2609.28594) cover bipartite orders up to 66 by SAT without a proof log. We know of no earlier witness-checked computation for these orders; the contribution is a recomputation with certificates and an independent audit. Nothing is claimed about the Erdős–Gyárfás conjecture itself or about orders above 68. What was checked. Controls reproduce Tranquilli's Table 2 at cap 29, the canonical class counts 1, 1, 3, 10, 31, 229, 2036 for v = 7..13 (equal to the nauty genbg sets; the auditor extended the comparison to v = 13 arbitrary root and v = 14 triangle roots), a full genbg enumeration for v = 7..15 (orders up to 30) finds no graph without a 4-, 8- or 16-cycle, a filter-off control (C16 off) finds the one self-dual 19-point configuration, and eleven further tamper kinds are rejected by all checkers. Independently audited by a different AI agent instance (AUDIT.md, ACCEPT_WITH_CORRECTIONS, nine corrections applied); no human audit. Tier C (exhaustive search plus witness checkers, no kernel check, no Lean); the Elenchus ledger gate exits 0 with no findings. Limitations. Unverified: the coverage lemma is argued in prose and checked against nauty only for v ≤ 13/14; the auditor's search shares the proposal schedule and path test with the producer (independent code, not an independent method); n(3,10) = 70 was not read in the original (only the triangle-rooted route at orders 62–68 depends on it); no full text of Ripatti 2017 was available; genbg at v = 16 was not repeated; a Python check of the arbitrary-root cap-34 stream never completed (two C checkers stand in). The 134,625,781 bytes of route-1 certificates are not in the bundle (names, sizes and sha256 are in the paper; they are regenerable).