Graph Reach Sets the Remote-Response Limit of Local Interatomic Potentials

Force accuracy cannot certify physical fidelity when a response depends on atoms beyond a model's graph reach. For finite-range local-energy message-passing models, we prove an exact architectural law relating interaction depth L to source-target graph distance d_G. When 2L - d_G < 0, attribute-to-force and coordinate force-response cross-derivatives vanish for every parameter setting, so training cannot recover the missing response. In Au2/MgO, increasing MACE depth from two to three blocks crosses this boundary, improves held-out DFT doped-undoped contrast, and activates aligned Al-to-Mg sensitivity. By contrast, a parameter-matched width increase leaves graph reach unchanged and does not recover the response. Increasing cutoff closes 57.0% of the predictive gap (95% interval, 55.2-58.8%), while a SchNet-style model reproduces the depth-width ordering. Ag-Pd exposes the complementary failure: graph-permitted models retain the wrong response direction or scale despite competitive force errors. The graph-reach law therefore provides a pre-training test of representability and separates architectural impossibility from failures of supervision or optimization.