16 Structural Theorems BCT Letter 11: Sixteen Parameter-Free Structural Theorems for the Meson Spectrum from BCT Void Geometry

The light meson spectrum—π, K, η, ρ, ω, K∗, η ′ , and φ—encodes the non-perturbative dynamics of QCD, and first-principles predictions of meson masses typically require lattice QCD simulations with fitted parameters. We present sixteen parameter-free algebraic identities—"structural theorems"—that connect the interstitial void geometry of the Body-Centred Tetragonal (BCT) lattice directly to meson masses, decay constants, and electromagnetic radii. Each theorem is an exact algebraic relation involving only the void radii roct = (√ 2 − 1)/2 and rtet = (√6 − 2)/4, the crystal coupling α0 = roctrtet/π, and the energy scale ΛQCD = 220 MeV. Results include: the Colour Correction Theorem giving mρ = mπ/(2√ α0)(1 − 3α0/2) = 775.5 MeV (+0.035%); the Kaon Theorem giving mK = 494.2 MeV (+0.1%); the U(1)A Anomaly Theorem giving mη = 547.5 MeV (−0.074%); the Void Asymmetry Theorem giving mω = 782.1 MeV (−0.070%); the Vector Geometric Mean giving mK∗ = 891.5 MeV (−0.28%); and the Singlet Anomaly Theorem giving mη′ = 955.5 MeV (−0.26%). The proton charge radius rp = 0.8386 fm (−0.33%) and pion charge radius rπ = 0.6580 fm (−0.16%) are also derived. All sixteen theorems are falsifiable: each predicts a specific number from geometry alone.