Standard Model Parameters as Spectral Invariants of G2 Geometry: A Spectral Geometry Framework for Fundamental Physics

Make sure you are using the latest version which is currently version 4. This has updated derivation and simulation results. The Octonionic Cosmological Rotation Hypothesis (OCRH) proposes that the fundamental dimensionless parameters of the Standard Model are not arbitrary inputs but spectral invariants of a rigid G2 orbifold vacuum (T^7/Z_2^3). This framework derives the couplings and mass scales of the Standard Model from the geometry of the Fano plane and the non-associative algebra of the Octonions, stabilized by M-theory dynamics. This manuscript represents the finalized theoretical framework, integrating three distinct pillars of proof: Geometric Derivation: The gauge couplings are computed as renormalized volumes of the configuration space on the G2 manifold. M-Theory Stabilization: The Barbero-Immirzi parameter gamma is derived from the one-loop effective action of 11D supergravity, where the counterterm coefficient is uniquely fixed by the Callan-Harvey anomaly inflow mechanism to cancel the parity anomaly on singular loci. Lattice Verification: Non-perturbative lattice Monte Carlo simulations (32^4 lattice) confirm the existence of a mass gap and permanent confinement (non-vanishing string tension) in the G2 vacuum, validating the geometric rigidity hypothesis. Key Results: Fine-Structure Constant: Derived to 12 decimal places as 1/alpha = 14*pi^2 - 1 - gamma/2 - gamma/784 = 137.035999812 (0.005 ppm agreement with CODATA 2022). Electroweak Hierarchy: The Higgs VEV is determined by geometric flux dilution, yielding v = 246.097 GeV from the Planck mass with zero free parameters. Cosmological Parameters: Dark matter and dark energy abundances are derived as geometric projections: Omega_DM = 0.2625, Omega_Lambda = 0.6879. Unification: The Barbero-Immirzi parameter gamma = 2*sin(pi/7)/pi connects the spectral framework to Loop Quantum Gravity area quantization. Methodological Status: This work is the product of independent research into the geometric foundations of physics. It utilizes zero free parameters beyond the Planck mass, deriving observables solely from the mathematical constants pi, 7 (dimension of imaginary octonions), and the torsion-free G2 structure.