The Unified Foam Field Theory derives all Standard Model observables from the geometry of a single truncated octahedron (Kelvin cell) with Oₕ symmetry and zero free parameters. The existing papers establish what is derived; this paper establishes why the derivations take the forms they do. The unifying principle is the local decision principle: the foam disturbance makes greedy local choices at each face junction with no knowledge of the global destination — exactly as electrical current propagates through a resistor network, taking the path of steepest local gradient at each crossroads rather than computing the globally optimal route. From this one principle, eight structural results follow: (1) the dihedral angle coupling between generations, explaining why K₁₂ ≠ K₂₃ and giving the tau mass formula m_τ = m_μ × exp (28 arccos (1/√3) / (3π) ) ; (2) the exact geometric progression r₁, Eg (4), r₂ from r₁ × r₂ = 16; (3) a direct spectral derivation of the muon mass as m_μ = mₑ × exp (r₁r₂/CA) = mₑ × exp (16/3) (0. 017% error) ; (4) a polaron derivation of the electron mass as an independent verification of the published formula; (5) the three-generations theorem — Oₕ has exactly three distortion irreducible representations, so exactly three fermion generations exist as a theorem of representation theory; (6) the identification of eight gluons with eight hexagonal face normals pointing along the (111) -family BCC nearest-neighbour directions; (7) the cell/void/either classification as the geometric origin of spin-statistics, with fermions (odd under the antipodal map) committed to the cell wall and bosons (even) able to propagate through either channel; and (8) the recording principle as the physical resolution of the quantum measurement problem without observers, many-worlds, or hidden variables. All results are consistent with and physically explanatory of the 47 previously published derivations. No new inputs are required beyond the existing framework.
Luke Martin (Wed,) studied this question.