Isomorphic Hadronic Resonators: Phenomenological Analysis of Discrete Mass Spectra via Non-Linear Ricci Curvature Phase Compression

Abstract

This paper presents a parameter-free phenomenologicalframework that derives discrete hadronic mass intervalswithin the Particle Data Group (PDG) registryfrom first principles. Instead of employing computationallyexpensive lattice QCD gauge configurations, thehadronic spectrum is modeled as an isomorphic systemof standing waves governed by a bounded QCD confinementresonator. We demonstrate that the characteristicmass steps, ΔMm ≈ 0.897 GeV for mesons andΔMb ≈ 0.612 GeV for baryons, emerge directly from thestandard QCD scale parameter ΛMS ≈ 0.330 GeV undernon-linear Ricci phase compression and four-dimensionalspace-time boundary conditions. The model successfullymaps heavy quarkonia and exotic multiquark configurationswith MeV-level precision. Furthermore, we definerigorous structural corridors of spectral exclusion(”hadronic dark zones”) between 4.1359 GeV and 4.1762GeV, establishing a strong, falsifiable hypothesis suitablefor experimental validation.