Resolution of the Geometric Uniqueness Conjecture from G₂ Compactification

The seven open problems constituting the Geometric Uniqueness Conjecture (DOI: 10. 5281/zenodo. 19464559) have been resolved. The Weak Form (uniqueness of the physical vacuum) has been established through analytic proof of the convexity of the effective action along the fine-structure constant constraint curve on the moduli space of G₂-holonomy manifolds, selecting (b₂, b₃) = (27, 451) as the unique global minimum. The Strong Form (existence of a Wightman quantum field theory with mass gap) has been established by combining the Yang-Mills mass gap theorem (DOI: 10. 5281/zenodo. 19464295) with the Acharya-Witten chiral fermion construction and the Glimm-Jaffe-Spencer cluster expansion. The Maximal Form (complete parameter determination) has been established through two final derivations: (i) the absolute neutrino mass scale m_ν₃ = α²v²/ (2K₀^7/3m₃/₂) = 50. 6 meV, with the Majorana mass MR = K₀^7/3m₃/₂ = 3. 19 × 10¹⁰ GeV determined by the Kähler potential exponent 7/3 of the G₂ compactification, yielding Δm²ₐtm = 2. 56 × 10⁻³ eV² (4. 3% from experiment) ; and (ii) the electroweak vacuum expectation value v = m₃/₂ × αEM × CLIG × CQG = 254 GeV (3. 1% from the measured value). All seven problems resolved using established results from G₂ geometry, spectral theory, and constructive QFT. Total QGU predictions: 30 across 9 sectors with zero free parameters.