Paper 44 of the Leveille Framework series. Using the dimensionless Cahn-Hilliard free energy for a spherical nucleus with diffuse interface, the critical nucleus condition yields the exact algebraic identity g* = 4π — the surface area of a unit sphere in natural units. In dimensional form this recovers ΔG* = 12πσδ³, mapping to ΔT ≈ 34.5 K in the homogeneous nucleation regime for pure water. Three limitations are named openly: the central temperature estimate is ~4 K warmer than canonical experimental values, the Arrhenius behavior of real nucleation-rate data presents a genuine challenge (though not a settled falsification given 16–25 orders of magnitude uncertainty in the kinetic prefactor), and the selection principle for why g* = 4π rather than another geometric factor remains an open conjecture. The Leveille Framework posits that exact zero tolerance is not physically realizable (Δ > 0) and derives consequences across domains.
Anderson leveille (Mon,) studied this question.