A Complete Solution to the Yang-Mills Existence and Mass Gap Millennium Prize Problem

Version 3 of the collected Yang-Mills preprints of the Eriksson programme,superseding versions 1 and 2. 64 papers, 670 pages, with a navigable outline and afront-matter manifest recording the archived version of every paper. READ THE ERRATA TABLE BEFORE CITING. Eleven of the 64 papers now carry aretraction, an erratum or a supersession notice on their own first page, includingone FULL RETRACTION (ai.viXra:2602.0052). Among the withdrawals: Theorems 1.1, 3.1and 4.1 of 2602.0033 are not established; Theorem 3.1 of 2602.0036 is notestablished and its Corollaries 3.2-3.3 are withdrawn; Theorems 1.1 and 3.11 of2602.0085 and Theorem 4.4 of 2602.0084 are retracted. The notices are the author'sown, published on the archive, and are tabulated in full in the front matter. SCOPE OF THE CLAIM. This volume assembles a CONDITIONAL construction. Relative todeclared external mathematics (abstract Kotecky-Preiss cluster expansion,Osterwalder-Schrader reconstruction, lattice reflection positivity) and to aninternal ledger of named hypotheses, the chain assembles OS0-OS4 and OS1 andreconstructs a Wightman QFT with a mass gap. Version 1 of this record was titled asa complete solution of the Millennium Prize Problem; that wording is withdrawn bythe author in the current Master Map (ai.viXra:2602.0096v2). No claim of a solutionto the Clay Millennium Problem is made here. CONTENTS.Part I - the 2602 series (32 papers, 374 pages): the conditional construction of 4DSU(N) Yang-Mills with a mass gap, via Balaban's renormalization group, log-Sobolevand Poincare inequalities, polymer/cluster expansions, large-field suppression,ultraviolet stability, and rotational symmetry restoration.Part II - the 2607/2608 series (32 papers, 289 pages): machine-checked results inlattice gauge theory, formalized in Lean 4 / Mathlib - a volume-uniform Wilson-looparea law, the exact two-dimensional SU(2) heat-kernel lattice model, Bessel-ratiocalculus for lattice gauge expansions, reflection positivity for Z_N lattice gaugetheory, Perron-Frobenius vacua and transfer-operator spectral gaps for the coupledZ_2 slice, a thermodynamic limit for local lattice gauge Gibbs states, and afinite-SU(2) trace-skein closure for Makeenko-Migdal crossing terms. WHAT CHANGED SINCE VERSION 2. An archive fault is repaired: ai.viXra:2602.0052previously served one paper's metadata with a second paper's PDF, forcing version 2of this volume to route around it; both records were re-uploaded on 2026-08-02 andevery paper now sits under its own identifier, with no workaround. Eleven papersacquired errata or retractions. The five manuscripts that version 2 had to label"submitted, not yet archived" now have identifiers (entries 94-98) and are ordinaryPart II entries: nothing in this volume is unarchived. Eleven records are new andeleven are at a newer version. RELATION TO THE COMPANION RECORD. This volume and the companion record10.5281/zenodo.18800920 (information recovery, coherence maintenance, and thequantum-classical boundary) partition the author's preprint corpus without overlap:64 papers here, 40 there, no paper in both. Every paper is reproduced as archived on ai.viXra, unaltered. Author page:https://ai.vixra.org/author/lluis_eriksson