SU(2) Yang-Mills: Spectral Bounds, Vacuum Concentration, and Criteria for the Continuum Limit

This deposit contains Version 5 of “SU(2) Yang-Mills: Spectral Bounds, Vacuum Concentration, and Criteria for the Continuum Limit,” together with its supporting research package and portable LaTeX sources. The manuscript investigates the physical transfer spectrum of lattice SU(2) Yang-Mills theory and the mathematical controls required to carry spectral information toward a continuum limit. It develops quantitative results concerning gauge-invariant states, the physical vacuum complement, representation truncation, vacuum concentration, and the compatibility of spectral estimates with changes of cutoff and spatial volume. The work presents explicit finite-volume spectral bounds and finite-matrix certification criteria with control of omitted representations. Vacuum-concentration estimates yield entropy bounds, quantitative fidelity obstructions for hard electric cutoffs, and necessary growth conditions for retained representation spaces. Local comparison estimates control fixed discarded-link sectors, while collective projection and Schur estimates identify the additional hypotheses required for a volume-uniform spectral bound. At fixed spatial cutoff and positive coupling, the manuscript constructs subsequential infinite-volume physical-time dynamics from local history correlations, with nonconstant gauge-invariant observables. It also presents exact-blocking results, corrected effective-potential theorems, and a representation-by-representation two-dimensional benchmark. A finite three-link conditioning functional is certified through Wilson coupling 0.354; its physical application remains conditional on the block-comparison hypotheses stated in the manuscript. The accompanying materials provide derivations, deterministic calculations, reproduction scripts, inputs, and supporting data. They include the reproduced winding-channel Monte Carlo study, coupled-replica analyses, and the exact verification of the 26-point Migdal-Kadanoff numerical grid. These components retain their respective mathematical and statistical scopes. Published glueball measurements remain attributed to their original authors, and algorithmic synchronization rates are distinguished from the physical transfer-operator spectrum. The results establish benchmarks and formulate precise continuum transfer criteria. A nontrivial four-dimensional spatial-cutoff construction and a positive spectral bound uniform along that construction are not established; no exact continuum mass is asserted. Aleksandar Mihajlovic is the sole author. The research received no external financial support, grants, or third-party sponsorship.