Universal Mass-Gap Formula ∆ = μ ln K: Exact Spectral-Chaos Scaling and Hadron Spectroscopy

Abstract

We propose a universal logarithmic scaling law for excitation gaps, ∆a(K) = μa ln K, where K ≥ 2 is the integer branch degree of exactly solvable chaos and μa is a sector-dependent physical calibra- tion scale. The mathematical origin of the logarithm is the exact regularity-resolved transfer radius K−s in Spectral Chaos Version 6, which gives the decay scale slnK. For one selected reflection- positive chaotic autocorrelation, a cyclic positive-transfer reconstruction has the exact continuous excitation threshold ħslnK/τ, after a time step τ is specified. Identifying this auxiliary scale with hadronic excitation energies is a physical hypothesis, rather than a theorem about quantum chromo- dynamics. We retain the comparisons with light mesons, charmonium, bottomonium, and glueball spectra in Figs. 1–4, including the light-meson prediction at K = 11 of 2682.0 MeV. The prime and composite assignments in these plots are phenomenological; noninteger coordinates are continuous interpolation parameters. The Supplementary Material separates exact dynamical results, known branch-algebra KMS structure, a conditional physical gap criterion, and the spectroscopy proposal.