The Native Lattice Graviton Is Not Massless: Ward Criteria and the Limits of Local Regge Repairs at κ = 1

The native Lorentzian Regge path sum on the four-dimensional Kuhn lattice fails the zero-momentum masslessness test at one loop. At identified κ = 1, with flat measure and Feynman damping on the eleven non-posting edge channels, its per-site transverse-traceless remainder does not have ordered limit zero. This is a theorem with no remaining mathematical premise; independent verification of its final composition is pending. It does not determine a finite particle mass. We organize possible repairs by an exact identity: the remainder is i/2 times the difference between second- and first-order Ward defects. Real weights cannot supply the missing vertex symmetry. Smooth corrections of cubic or higher order in the deficits leave the one-loop remainder unchanged at fixed slope and weight. Area-additive charges reduce to one even-curvature parameter, whose tested values fail numerically. More general local charges retain eight relevant area derivatives when their flat even curvature vanishes. Their corner condition is exact, while cancellation of their integrated remainder and restoration of their classical second-order identity have different evidential status. These results delimit local repairs; they do not prove a universal prohibition on every local charge. A successful repair must derive its coefficients and pass the summed Ward test on every transverse-traceless probe. Companion to Quantum Gravity from the Recognition Ledger (https://doi.org/10.5281/zenodo.23839819). Preprint of the Recognition Physics Institute, 14 pages. Not peer reviewed.