True Flat Hessian Weights for the 4D Regge Action on the Freudenthal–Kuhn Lattice

We report the kernel-checked derivation of the flat second variation of the four-dimensional Regge action on the Freudenthal/Kuhn triangulation of the integer lattice, obtained from geometry alone. Fifteen nonzero 0/1 edge classes of the unit 4-cube organize the discrete metric. Per-hinge Gram-projection cosines supply dihedral derivatives at flat. Four lattice orbits of triangle hinges admit exact 2π flatness of their stars. Orbit counts, Heron area gradients, and star deficit kernels assemble into true class weights. At zero momentum those weights kill transverse-traceless, gauge, trace, and homothety probes identically, while a provisional weight-1 aggregate evaluates to 32 on the same gauge decoy. At leading order in momentum, the (1,1)-orbit Bloch symbol along (1, 1, 0, 0) evaluates to −3 on the axis TT probe and exactly 0 on pure gauge. Every statement is tagged THEOREM, MODEL, or OPEN against named Lean 4 declarations in IndisputableMonolith. Continuum recovery of the Einstein-Hilbert action in four dimensions remains OPEN.