The Gravitational Gap and the Kinetic Clutch: Structural Proof and Substrate Requirements for Dark Matter Detection-SNSFL-GAMCollider

Every major direct-detection experiment for dark matter — LUX, XENON1T, XENONnT, PandaX-4T, LZ (417 live days, 2025), CDMS, CoGeNT — has returned a null result. We prove this is not a measurement problem. It is a structural necessity. The B-axis of dark matter (Bᴸᴹ = Ωdm ≈ 0.269) is gravitational. Every detector element ever used is electromagnetically active (Bdet > 1.0). The GAM Collider fusion rules produce τout ≫ TL = 0.1369 at all physically reachable bond parameters. No stable state forms. No signal. Not by accident — by structure. We then derive the structural requirement for detection and identify four material candidates — one operable at room temperature — using the same formal framework. The Lean 4 proof corpus is archived at DOI:10.5281/zenodo.18719748 with 0 sorry throughout. No physics PhD is required to follow the argument. The long division does the work.