Dark Matter Passes Through Electromagnetic Detectors Because It Must: A Formally Verified Geometric Axiomatic Module-GAM Collider Analysis

Every major direct detection experiment for dark matter LUX, XENON1T, XENONnT, PandaX-4T, LZ (417 live days, 2025), CDMS, CoGeNT, and DAMA/LIBRA has returned a null result despite reaching unprecedented sensitivity. We prove that these null results are not a measurement problem. They are a structural necessity. Within the Substrate-Neutral Structural Foundation Theory (SNSFT) framework, dark matter is formally represented as the Darkmatter element (Dm): a B-dominant primitive with BDm = Ωdm ≈ 0.269 encoding gravitational coupling and no electromagnetic interaction. Every element used in current detectors (Xe, Ge, Si, Fe, NaI) has Bdetector ≫ BDm, encoding strong electromagnetic activity. The GAM Collider fusion rules formally verified in Lean 4 with 0 sorry compute the torsion τ = Bout/Pout of any two-element collision. For Dm+Fe at bond parameter k = 0: τ =BDm + BFe Pout = 0.269 + 3.5 Pbase/2 ≈ 7.63 The torsion limit is T L = ANCHOR/10 = 0.1369. The ratio τ /T L ≈ 55.7 the interaction shatters immediately. No stable bound state forms. No energy is deposited. No signal. The same-B necessity theorem (proved in the Noble Materials Map corpus) requires B1 = B2 for any stable (τ = 0) interaction. Dark matter's gravitational B-axis (≈ 0.269) cannot match any EM-active element's B-axis (> 1.0) at physically reachable bond parameters. We derive a specific, falsiable prediction: detection requires a substrate with Bdetector ≈ 0.269 ± 0.05 gravitational-regime coupling, minimal EM activity. No current experiment satises this. The Lean 4 proof corpus is archived at DOI:10.5281/zenodo.18719748. Keywords: dark matter, direct detection, formal verication, Lean 4, PNBA, torsion, GAM Collider, null results, B-axis incompatibility, substrate-neutral