7 Predictions — baryons BCT Letter 7: A Parameter-Free Baryon Spectrum from Vacuum Geometry — Seven Masses to Sub-0.3% from BCT Void Radii

Baryon masses are among the most precisely measured quantities in particle physics, yet firstprinciples calculations of the proton and neutron masses from QCD remain computationally demanding and rely on lattice QCD simulations with fitted parameters. We derive seven baryon masses—proton, neutron, ∆(1232), N ∗ (1440), N ∗ (1535), N ∗ (1520), and ∆∗(1600)—to sub-0.3% precision from the void geometry of a body-centred tetragonal (BCT) lattice, using zero free parameters. Three Regge coefficients built entirely from the void radii roct and rtet determine baryon masses via the universal Regge relation m2 B = m2 ρ + 2πΛ 2CB: the proton coefficient Cp = (1 + rtet − roct)/π = 0.9053, the neutron coefficient Cn = Cp + 2α0 = 0.9201, and the ∆ coefficient C∆ = πCp(1 + 8α0) = 3.013. The results are: mp = 936.1 MeV (−0.21%), mn = 940.6 MeV (−0.09%), m∆ = 1231.9 MeV (−0.008%), mN∗ 1440 = 1441.3 MeV (+0.09%), mN∗ 1535 = 1534.8 MeV (−0.016%), mN∗ 1520 = 1517.3 MeV (−0.18%), and m∆∗ 1600 = 1603.5 MeV (+0.22%). The ∆(1232) prediction at −0.008% is among the most precise parameter-free hadronic predictions in the literature.