Lorentz γ from Foam Wave Kinematics: A Coordinate Substitution and its Corollaries

In the existing UFFT corpus, Lorentz invariance is established by three routes, none of which derives γ kinematically. The Core Framework v9 §"Lorentz Invariance" asserts covariance structurally (the foam is spacetime; ρ transforms covariantly with g_μν). Paper #59 §6.2 reaches Lorentz invariance by renormalization-group flow (O_h → O(3) lattice artefacts are dim-6 RG-irrelevant, Wick rotation produces SO(3,1)). Paper #60 §4.3 uses Weinberg–Witten on the continuum's Lorentz covariance as input to nonlinear GR. In all three routes, γ itself enters as a borrowed special-relativistic quantity, for example in the Klein–Nishina formula of From Foam to Fermions Ch 35.A single coordinate substitution ξ = γ(x − vt), y' = y, z' = z applied to the foam wave operator □φ = (1/c²)∂²_t φ − ∇²φ acting on a uniformly moving point defect reduces □ to the negative Laplacian in (ξ, y', z') if and only if γ²(1 − v²/c²) = 1, which defines γ. Four corollaries follow from the same substitution: length contraction L = L₀/γ, time dilation τ = γτ₀, relativistic field contraction (perpendicular ×γ, parallel ×1/γ² after Lorenz-gauge bookkeeping), and the SO(3,1) boost-subgroup closure law w = (u + v)/(1 + uv/c²) with γ_w = γ_u γ_v (1 + uv/c²). Applied to a uniformly moving Schwarzschild source the substitution produces the full linearized moving-Schwarzschild metric exact in v/c, including gravitomagnetism h_tx ~ γ²v · (2GM/rc²); frame-dragging is an algebraic corollary. Applied to a rotating mass the substitution produces the leading Kerr gravitomagnetic dipole h_tφ ~ GJ/(c²r²) at long range. Finite-size corrections via the BCC lattice □ recover the same O_h-quartic operator Δ_4(k) = Σ k_i⁴ − (3/5) k⁴ that drives the δc/c ~ (E/E_P)² prediction in Paper #59 §6.2. The two routes agree on operator content and on scaling, providing independent kinematic confirmation. The canonical electron mass formula m_e = r₁ M_P exp(−(E−F)(2Δ+√Δ)/16) factors as a walk action S_walk = (E−F)·(2Δ+√Δ)·C_A/|G| over the foam, giving the cell-integer formula a physical interpretation consistent with the substitution's propagating-wave picture. The full Lorentz group SO(3,1) is recovered from foam dynamics without invoking Wick rotation. Numerical verification is performed at machine precision throughout.