The Bridge-Contract Criterion: A Form Audit for Transport Arguments, with an Instantiation in the abc Literature

Abstract

The abc Gap Series: Part 2— The Bridge-Contract Criterion This ongoing research project proposes a seven-component bridge contract and a versioned ledger audit for transport arguments and global-only claims. The current paper reports a retrospective two-case illustration of the frozen v1-T transport ledger and one selected-rows instantiation in the abc literature. The criterion judges contract form and the presence and addressability of obligations, not mathematical truth. A served ledger does not prove the underlying claim. The current research state aligns the C7 illustration with all five hypotheses of the unchanged contract definition. Admissibility (H1), container order (H2), monotonicity (H3), compatibility (H4), and the target bound (H5) give the conditional chain ν_q(x) = ν_C(i_q(x)) ≼ ν_C(i_Θ(y)) ≼ τ_Θ and hence membership in the lower target set H_Θ. All load-bearing hypotheses require proof addresses. An identity countermodel refutes the earlier incomplete diagram implication, not Definition 2.1. The LANA comparison now distinguishes numerical readout equality in V from container order in C. Equality of identified container images gives H2 by reflexivity; numerical equality alone requires an additional order-reflection or addressed-order bridge. Target membership also requires H5 and the other applicable hypotheses. No IUT-to-C7 transfer is established. Current Parts 4–6 refine normalization and quantity-consumer obligations while retaining the historical v0.2 audit pins. Under the stated same-field, all-place, archimedean and all-L× hypotheses, standard-modulus rigidity concerns final effective weights β = aλ and permits constant global factors including j². A linear quantity family requires y-independent q_v, a defined reference sum and finite sums or justified absolute convergence; its identification with a classical reference remains an additional bridge. Coordinate, field, period, hull, measure and log-volume applications remain open where the cited hypotheses have not been established. The retrospective raw matrix and its two visible dissents remain version-bound illustrations. Different reported source types and audited versions limit their comparison; 10/12 agreement is not a reliability, discrimination or false-alarm estimate. The paper supplies no RH-side verdict, general methodological validation, new empirical evidence, computation or Lean proof, or overall ATS, abc, IUT or LANA proof verdict. ─────── ✦ ───────seriesdirectory (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: A Form Audit for Transport Arguments, with an Instantiation in the abc Literature — DOI 10.5281/zenodo.21960476 (latest version) ↳ 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: What the Product Formula Allows: A Rigidity Theorem and an Effective-Weight Test for the ATS Height Subchain — DOI 10.5281/zenodo.21952486 (latest version) ↳ coming soon - 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) ℹ Companion (meta) paper: From Landscape to Atlas: Multi-Route Cartography of an Ongoing Expedition Toward the abc Conjecture (formerly: The abc Landscape) — DOI 10.5281/zenodo.21916900 (latest version). The atlas paper is the complete memory of all routes; the series parts and capsule papers present selected results as independently citable units. Changes since v0.2 — v0.3 Corrects the C7 illustration: H4 states compatibility identities, H5 supplies the target bound, and the five hypotheses appear separately. The bounded identity countermodel concerns the old incomplete diagram implication; the seven-component definition and historical raw audit codes remain unchanged. Both illustrations receive layout repairs without changing their texts or formulas. Corrects the typed G11/LANA consumer: readout equality in V does not automatically establish H2 in C or target membership. Object, domain, quantifier, direction and target-bound obligations remain separate. Restricts the historical F-R6b definitional reading to its named audited normalization framework; it is not an unconditional identification across ATS fields or volume constructions. Adds current research references to Part 4 v0.3, Part 5 v0.3 and Part 6 v0.3, alongside the retained historical v0.2 audit pins. Clarifies standard-modulus/effective-weight rigidity and linear-family, reference, convergence and domain assumptions, without assigning new retrospective audit verdicts. Clarifies F/P source-type asymmetry and statistical limits while retaining both raw dissent pairs. Updates the Part 6 series title and preserves its concept DOI link. Documents the intervening synoptic presentation recorded on 20 August, the two illustrations recorded on 18 September, and the September styling changes. These presentation developments are distinguished from the current scientific corrections. Preserves the published v0.2 PDFs and separately binds the later local manuscript baseline. The exact TeX used for the public v0.2 PDFs has not been recovered. The F/P comparison and T/F crosswalk were already documented on 16 August, before publication; they are not presented as new post-publication evidence.