The Geometric Uniqueness Conjecture: Towards a Parameter-Free Determination of the Laws of Physics from G₂ Compactification

A conjecture has been formulated asserting that the laws of four-dimensional physics are uniquely determined by a single compactification geometry in eleven-dimensional supergravity. Three nested forms have been stated: (Weak) a unique pair of Betti numbers (b₂*, b₃*) minimises the effective action on the moduli space of compact G₂-holonomy manifolds; (Strong) the dimensional reduction at this minimum produces a Wightman quantum field theory with gauge group SU (3) × SU (2) × U (1) and a mass gap Δ > 0; (Maximal) all coupling constants of the resulting theory are uniquely determined by (b₂*, b₃*) with no free parameters. Evidence has been drawn from the Quantum Geometric Unification (QGU) programme: twenty-eight Standard Model parameters have been derived from the candidate vacuum (b₂, b₃) = (27, 451) with a mean deviation of 2. 3% from experiment and a Bayes factor B ≈ 10³⁹. The Yang-Mills mass gap — a Clay Millennium Prize Problem — has been established as a special case of the Strong Form. The conjecture has been decomposed into seven open problems: (1) classification of compact G₂ manifolds; (2) analytic proof of thermodynamic uniqueness; (3) non-perturbative construction of the G₂ QFT (subsuming the YM mass gap) ; (4) derivation of αEM from Betti numbers; (5) completeness of coupling constant determination; (6) uniqueness of the Higgs potential from G₂ geometry; (7) stability under quantum corrections. Falsification criteria have been identified. The conjecture asks whether the fundamental constants of nature are mathematical theorems rather than empirical measurements.