This release contains Versions 13.1–13.5 of the Zsa-G Framework research program. The series develops a constructive spectral approach to the infrared sector of non-Abelian gauge theories. Beginning with the resolution of the Gribov horizon through measure concentration and resolvent-enhanced spectral localization, the framework proceeds through dimensional transmutation, confinement mechanisms, BRST structure, and spectral threshold formation. A central result of the series is the derivation of a leading-order spectral threshold in the color-singlet sector generated by the non-perturbative infrared scale γ. The work explicitly distinguishes between a leading-order spectral threshold and a complete all-orders proof of the Yang-Mills mass gap. The final paper (V13.5) identifies the analytical limits of continuum functional methods and formulates the transition toward numerical lattice validation as the next stage of the research program. V13.1The Gribov Horizon and Measure Concentration Spectral horizon penalty Measure concentration Boundary suppression Resolvent stability Dunford-Taylor contour protection V13.2Dimensional Transmutation and the Dynamical Generation of the Spectral Gap Localization of the horizon operator Modified Callan-Symanzik flow Dimensional transmutation RG invariance of γ Thermodynamic gap equation V13.3Confinement, Osterwalder-Schrader Positivity, and BRST Structure Complex pole structure OS positivity violation BRST cohomology Kugo-Ojima mechanism Observable color-singlet sector V13.4From Horizon Dynamics to Spectral Threshold Formation Composite correlators Landau singularity analysis Branch-point formation Leading-order threshold Constructive mass-gap mechanism V13.5From Spectral Thresholds to Numerical Validation Stability beyond leading order RG protection arguments DSE/BSE truncation problem Necessity of lattice verification Transition toward numerical validation
Zsa Zsa Gersina (Thu,) studied this question.