Yang-Mills spectral and state maps: finite-regulator calculations and continuum research checkpoint

Abstract

This Yang–Mills research edition brings together five readable manuscripts, their complete selected mathematical sources and reproducible finite checks. Start with quantum_coarse_graining.pdf (79 pages), then use YM_CURRENT_READING_GUIDE_20260909.md to choose the relevant companion: interacting tensor-band calculations (71 pages), the non-Abelian vertex calculation (63 pages), volume-independent vacuum estimates (81 pages), or spatial-continuum maps and obstructions (129 pages). Component readers are explicitly dated snapshots, with their matching sources retained separately from the current cumulative text. The calculations retain the finite SU(2) Wilson Hamiltonian, physical couplings, gauge constraints, actual interacting vacuum, raw state norms and spectral measures. They give finite-regulator state and operator maps, cubic/tensor and local-energy calculations, gauge-curvature maps from specified forced fluid profiles, and precise estimates for the proposed volume, coupling and continuum paths. The spatial reader includes the shrinking sufficient analytic disk at fixed coupling; the volume reader retains the endpoint asymptotic and explains exactly what its first-moment estimate does and does not control. The full interacting four-dimensional continuum and the mass-gap question remain unresolved. No Millennium problem solution is claimed. The source ZIP contains the complete selected proof texts, their recursive TeX inputs, original component snapshots, exact programs and recorded outputs. A source manifest, reader-provenance record and AI reading index identify the documents and their byte-level checks. These finite checks and packaging checks do not independently certify every analytic theorem. The exploratory incomplete full-L2 tensor contraction is not included as a certified coefficient calculation. A closing math-delimiter typo in the volume TeX was repaired for this edition without changing its mathematical formulas. All 13 assets of the previous published version remain unchanged. In particular, its complete mixed Overleaf archive is a historical capture at commit c501b11ff6caf6db195e5dc06b2b22724e886955; it is not relabelled as the current project. The new selected Yang–Mills packet is the later continuation. Private user logs, account paths, credentials and copied literature collections are not new release inputs. GitHub reading and source mirror. The S6 topology and degeneration archive and corrected 208-page Navier–Stokes reconstruction retain their own DOI collections. Existing authorship, primary-source attributions, license scope and prior publication history are preserved. These are AI-assisted research and reconstruction records intended to make the detailed work inspectable.