G2 Geometry Predicts All Standard Model Parameters: A Zero-Free-Parameter Framework

This preprint presents a theoretical framework in which all Standard Model particle masses, mixing angles, and coupling constants are derived geometrically from a single G2 octonion field undergoing a topological vortex condensation in the early universe. The condensation produces exactly six active vacuum orientations at 60-degree intervals, from which precisely three stable particle loop sizes emerge — corresponding to the three observed generations of matter — with no free parameters beyond the Planck mass.

The framework yields over 30 numerical predictions matched against PDG experimental values. Three are independently verifiable with a pocket calculator and are presented on pages 11-12: the proton mass (predicted 939.0 MeV, measured 938.3 MeV, error 0.08%), the neutrino mixing angle theta_13 (predicted pi/21 = 8.571 degrees, measured 8.57 degrees, error 0.02%), and the hydrogen ionisation energy (predicted 13.6057 eV, measured 13.6057 eV, error 0.000%). Additional predictions include new particles accessible to existing LHC searches: a chi familon resonance at 94.6 GeV in the dijet channel, and supersymmetric partners at 391 GeV and 684 GeV.

The document is structured in four parts: an accessible introduction with the three verifiable predictions (Part 1, pages 1-14), the physical and geometric foundation (Parts 2 and 3), and the full mathematical derivations with the complete prediction table (Part 4)

What's new in v6 (compact)

• Operator-assignment joint closed. The deepest open joint — why a mode-count reads the Dirac η and a mass-form reads the signature η — is now settled by explicit computation on L(3,1)=S³/ℤ₃: the two standard operators give different values (signature → −2/9 = φ_K, Dirac → −2/3), proven distinct by a ℤ₂ cross-test (signature defect 0 vs Dirac −1/2). The assignment is forced by the observable's nature, not chosen. φ_K = 2/9 is now a completed computation; 7/102's pieces are all forced.
• δ_χ = 2/105 fully decomposed. Computing the ℤ₃ normal-bundle η returns 2/9 (not 105) — showing 105 is an Ambrose–Singer product, not a lone η: a computed phase (2/9) × a channel-count amplitude ε² = 3/35. Dissolved a 5-vs-4 category error.
• ε² = 3/35 computed as a combinatorial probability. ε² = (N_c/N_Fano)(1/5) = (3/7)(1/5), factorizing spatial × coupling, with the neutrino 1/44 = (1/11)(1/4) as an exact structural parallel. Explains why it's rational.
• Code/text consistency fix. Removed a stale eps_q = 0.0451 hardcode; the verification program now demonstrates the single derived ε = √(3/35) driving both the quark ladder (m_c/m_t = ε⁴) and neutrino θ₁₂. One input (M_Pl), one derived ε — claim and code now agree.
• Referee-cycle corrections applied. τ₀ demoted to "canonical, over-determined by one object" (weight×path a forced reading, not independent); 9/25 grounded in the forced 5 = 14−8−1 generator count; f_K scope narrowed to the pseudoscalar octet; honest-label calibration throughout.
• Rewritten abstract (headlines first, ε compressed), cleanup: ToC now starts on p2, fixed references and overflow, corrected the dependency-graph figure (ε now shown derived, not measured). 38 pp, 35/35 observables pass, 22/22 snippets run.