The Hadron Spectrum from Icosahedral Confinement and Twin Prime Promotion
Abstract
Starting from the proton's three-phase icosahedral structure on a mod-24 lattice, we derive the masses of eleven hadrons with a mean error of 0.32% and zero adjustable parameters. Three colour channels (RED, BLUE, GREEN) can each independently promote to the next twin prime bridge beyond the confinement boundary at position 19, generating a 2³ = 8 power set of baryon states. A selection rule forbids GREEN-only promotion (confirmed by the absence of any baryon near 1032 MeV), while the RED+GREEN state predicts the Λ(1405) to 0.03%. The decuplet spectrum follows from icosahedral tiling frustration with exact doubling at each successive promotion. The Ω⁻ serves as a Rosetta Stone: two independent models (colour-specific promotion and anonymous period-stretching) converge on its mass, traced to the identity 29 + 41 + 59 = 3 × 43 linking three twin prime bridges to the next Heegner number. The framework produces 11 matches, 2 predictions, and 1 confirmed forbidden state from derived geometry alone.
Fields of Study & Subjects
Quantum Chromodynamics and Particle Interactions
Nuclear physics research studies
High-Energy Particle Collisions Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 28 February 2026
- Document type
- Preprint