The Bridge Certificate Applied to the Joshi ATS Series: A Ledger Audit (DRAFT)

Abstract

DRAFT / work in progress. This is a versioned working paper of an ongoing research programme; newer versions supersede older ones. No claim about the truth of the abc conjecture, the correctness of IUT, or the correctness of the ATS series is made. We audit Kirti Joshi's Arithmetic Teichmüller Space (ATS) series — a detailed, publicly available repair programme for the disputed transport step of Mochizuki's Corollary 3.12 — against the bridge-certificate standard of this series (Parts 2–3). The audit is a pre-specified four-row form test (ledger rows R2, R4, R6, R8, fixed in the audit mandate before the test), not a complete certification and not a proof audit. On the four pre-specified form questions, the publicly posted text supplies three requested forms of explicitness: a numerically explicit theta-link transport law with the j²-factor carried visibly; an explicit assignment of the j²-load to a compensating renormalization forced by the product formula; and an expressly declared, asymmetrically used second mode (the global Frobenius shift). The fourth row remains split: the source states the order relation with a written-out proof whose core step is addressable, but the cross-container compatibility carrying the abc conclusion is set by an identical global normalization rather than derived, and the source itself restricts the claim to the summed, global level. Dated external status notices from later parts of this series are recorded separately from the form verdicts. The audit measures auditability and contract form; verbatim source anchors are given for every verdict. Part 4 of the abc Gap Series. The abc Gap Series — series directory (each part lists the whole series; planned parts are updated with title and DOI upon publication): Part 1: The Gap in IUTchIII, Corollary 3.12 — DOI 10.5281/zenodo.19960781 (latest version) Part 2: The Bridge-Contract Criterion: Admissibility Tests for Transport Arguments and Globally-Summed Positivity Claims — (planned) Part 3: The Bridge Certificate — DOI 10.5281/zenodo.21925803 (latest version) Part 4: The Bridge Certificate Applied to the Joshi ATS Series: A Ledger Audit — DOI 10.5281/zenodo.21951155 (latest version) Part 5: The Joshi ATS Series under the Bridge-Certificate Standard: A Targeted Substance Audit and an All-Place Rigidity Classification of Effective Normalization Weights — DOI 10.5281/zenodo.21956398 (latest version) Part 6: Repairing the ATS Chain? A Rigidity Theorem for Product-Formula Weights and an Effective-Weight Test for the Height Subchain — DOI 10.5281/zenodo.21952486 (latest version) Part 7: The bridge certificate applied to our own programme (self-application; working title) — (planned; appears in sync with the landscape paper) Tool supplement: The Global Normalization Contract Lemma — DOI 10.5281/zenodo.21924253 (latest version) Companion (meta) paper: The abc Landscape: Obstructions, Failed Routes, and HCT Diagnostics — DOI 10.5281/zenodo.21916900 (latest version). The landscape paper is the complete memory of all routes; the series parts and capsule papers present selected results as independently citable units. The manuscript is provided in English and German, plus a combined file (English first, then German).