Volume-Independent Local Transfer Gap for Strong-Coupling Lattice Gauge Theory via Poincaré-Dobrushin Machinery

We establish a volume-independent local transfer gap for Wilson lattice gauge theory with compact simple gauge group in the strong-coupling regime. Connected Euclidean-time correlations of fixed gauge-invariant local observables decay uniformly in the lattice volume. For the continuum theory on four-dimensional Euclidean space, the Osterwalder-Schrader reconstruction step remains conditional: exponential clustering with uniform physical normalization would imply a continuum mass gap, but that continuum transfer is not claimed as completed here. The proof works through a renormalized free-energy functional over the lattice-regularized gauge-field measure and proves strict convexity in the Dobrushin-Zegarlinski strong-coupling regime. The full time-slice L^2 operator gap is isolated as a separate closure/tensorisation bridge rather than treated as an immediate consequence of the local transfer estimate. Changes in Version 2.6 (June 2026) Major: The main theorem and title are reframed from a broad strong-coupling spectral-gap statement to a volume-independent local/zylindersector transfer-gap statement for fixed gauge-invariant local observables. The full time-slice L^2 operator gap is kept as a separate closure/tensorisation bridge rather than an immediate consequence. Major: The conditional continuum/RG bridge is tightened: polynomial-LSI and gap-transport claims are stated as criteria or diagnostics with explicit OS/RP, transport, and summable-defect hypotheses, not as completed mass-gap transfer. Minor: The German version was resynchronized with the English leading version, remaining English section/proof text was translated, and the combined PDF metadata and German text layer were rechecked for real umlauts. Guardrail: The new OS-Capacity-Ledger v2 adds source-kind, OS-dangerous-capacity, circularity, RP-cone, and repair/cofactor status fields. It is documented as a control ledger only and introduces no Yang-Mills mass-gap claim upgrade. Files: English, German, and combined bilingual PDFs should be uploaded synchronously after GitHub sync and final preflight. Changes in Version 2.5 (May 2026) Minor: Dedicated source check integrated: connected FST/Yang-Mills/RH/RFEP self-citations were moved from version-specific Zenodo record DOIs to stable Concept DOIs where appropriate, and related 2026 preprint titles/DOIs were synchronized with current Zenodo metadata. Minor: The German bibliography was corrected against Crossref for Balaban's 1985 lattice gauge theory article; one stray uncited German-only bibliography item was removed. Files: English, German, and combined bilingual PDFs were rebuilt from the source-checked v2.5 release. Changes in Version 2.4 (May 2026) Major: English style and claim-guardrail pass integrated: RP, RG, reconstruction, and transport formulations were tightened so that continuum, reflection-positivity, and Osterwalder-Schrader steps remain explicit open bridge tasks rather than completed routes. Minor: Bibliographies were compacted to remove nearly empty final bibliography pages; German keywords and PDF metadata were localized and cleaned. Files: English, German, and combined bilingual PDFs were rebuilt from the current sources; no new mathematical or bibliographic claims were introduced. Changes in Version 2.3 (May 2026) Minor: German-language PDF hygiene pass: visible transliterated umlauts were normalized to real German umlauts, and the German source was rebuilt. Minor: English, German, and combined bilingual PDFs were rebuilt from the current local sources and renamed from the former Skeleton file stem to FST-YM_YangMills_MassGap_*; no mathematical claim change. Changes in Version 2.2 (May 2026) Critical: Adversarial review 2026-05-07 integrated: the Kingman route was downgraded from a standalone mass-gap proof to a diagnostic plus summable-defect criterion; Wasserstein-RG is explicitly conditional on a new quantitative SU(N) typical-set transport theorem. Major: Post-Zookeeper transfer section added and synchronized in English/German: the lattice gap and area law are now framed as the main path, while Zookeeper and RFEP are used only as normal-form and transfer-checklist constraints, not as an automatic continuum proof. Major: RFEP v1.8 normal-form checklist integrated: the text now separates strong-coupling/lattice evidence from the still-open continuum/Osterwalder-Schrader transfer. Minor: Hyperref target prefixes added for stable combined-PDF links; stale build logs removed; EN/DE PDFs rebuilt and combined into a bilingual PDF. Files: Version 2.2 was published with English, German, and combined bilingual PDFs. Changes in Version 2.1 (March 2026) Major: Doeblin-minorisation analytical route to λ<0 (Remark rem:doeblin-analytical): 4-step programme reducing analytical proof to establishing Doeblin constant α(β)>0 for SU(2) block-spin kernel. Minor: Bougerol–Lacroix (1985) reference added. Minor: Duplicate label fix (eq:typical-set). Changes in Version 2.0 (March 2026) Critical: Fixed \thanks placement (was outside \author group).