The Strong CP Angle as an Index Phase, the Quark Mass Determinant, and the Neutrino Mass Sector from the Rendering Algebra R12

Abstract

We resolve the strong CP problem and derive the absolute neutrino mass scale from the R12 rendering algebra of Array Cosmology (AC) with zero free parameters.

The QCD vacuum angle θ is shown to be exactly zero as the unique value satisfying both the closure relation e1e2 · · · e12 = −1 (which restricts θ to multiples of π/6) and the parity pair relation ek · ek+6 = Znoise ·1 (which further restricts θ to multiples of
π), with θ = π excluded by experimental CP conservation. Thermal corrections give |θeff| ∼ Z12 noise ≈ 8 × 10−13, two orders of magnitude below the current experimental bound. The prediction that no axion exists is falsifiable. The heaviest neutrino mass
is derived as m3 = me Z b0 noise/(1 − Znoise), where me is the electron mass, Znoise = (π − 3) ln 2 is the vacuum Landauer noise, and b0 = 7 is the QCD one-loop betafunction coefficient. This yields m3 = 0.0497 eV, matching p ∆m2 atm = 0.0495 eV
to 0.35% and predicting normal mass hierarchy with Pmi = 0.054 eV, testable by JUNO, Project 8, and CMB-S4.