GIFT v2 : Geometric Information Field Theory

The Standard Model contains 19 free parameters without theoretical derivation. This work explores whether dimensionless observables may emerge as topological invariants from E₈×E₈ gauge theory compactified on seven-dimensional manifolds with G₂ holonomy. The framework predicts 43 observables (34 dimensionless, 9 dimensional) with mean deviation 0.13% from three geometric parameters.

A principal contribution of this version consists in explicit construction of the K₇ metric with G₂ holonomy via Twisted Connected Sum, including complete harmonic form bases for gauge (H²(K₇) = ℝ²¹) and matter (H³(K₇) = ℝ⁷⁷) sectors. The metric ansatz provides transition functions, coordinate patches, and gluing conditions, establishing the geometric foundation for dimensional reduction. Explicit harmonic 2-forms decompose into SU(3)_C (8 forms), SU(2)_L (3 forms), U(1)_Y (1 form), and hidden sector (9 forms). Harmonic 3-forms yield quark (18), lepton (12), Higgs (4), and right-handed neutrino (9) modes, with remaining forms (34) as dark sector candidates.

The framework yields exact topological relations: N_gen = 3 from rank(E₈) - Weyl = 8 - 5, δ_CP = 197° from 7×dim(G₂) + H* = 98 + 99, m_τ/m_e = 3477 from dim(K₇) + 10×dim(E₈) + 10×H*, and m_s/m_d = 20 from p₂² × Weyl. Additional predictions include complete neutrino mixing (mean deviation 0.13%), gauge couplings (<0.3%), and cosmological parameters (Ω_DE = ln(2) × 98/99 = 0.686146, deviation 0.21%). The 21×e⁸ dimensional transmutation mechanism predicts v = 246.87 GeV (deviation 0.26%) and quark masses (mean deviation 0.28%).

Several aspects require further development. The theoretical foundation for certain phenomenological formulas remains incomplete. The connection between topological structure and particle physics, while mathematically consistent, may represent coincidence rather than fundamental principle. Falsification criteria include fourth generation discovery or δ_CP deviation from 197° at high precision, testable in upcoming experiments.