We formalize a mandatory energy cost for geometric deformation of spacetime, expressed by the gatekeeper equality R = W / D(Phi), where W is the work required to produce a deformation measure Phi and D is positive-definite and vanishes if and only if Phi = 0. A signed resistance term that supplies restoring force on both sides of an equilibrium density is inserted as additive pressure support. A phase-diagram diagnostic with stiffness s = 20 places slope dominance near x ≈ 1.08 and value overtaking near x ≈ 1.51. The same nuclear-matched constants produce a resistance pressure of approximately 5.6×10^18 dyn cm^{-2} at solid density, exceeding self-gravitational central pressure by at least eight orders of magnitude for objects up to 1000 km radius, with no retuning. First-order Hartle frame-dragging on locked effective-density profiles yields modest, equation-of-state-dependent increases in moment of inertia (a few percent for SLy, approximately 8 percent for APR4). Controlled dynamical-collapse evolutions under the same locked parameters produce finite-density reversal and a drop in central Kretschmann scalar on the resistance-on side for configurations above a density and stiffness threshold, while matched pure-GR controls continue to collapse. Inspiral-pinned ringdown residual stacking on public gravitational-wave events returns noise-floor results (normalized residual energy consistent with 1), establishing a measured sensitivity limit rather than a detection. The signed resistance term is therefore stated as an open prediction: it produces faster ringdown decay than the inspiral-pinned general-relativistic quasinormal mode once a hierarchical stack reaches adequate aggregate signal-to-noise, or else the data place a tight upper bound on the stiffness. The present null constrains only the current method class and sample. The skeleton covers classical geometric grids from nuclear through atomic density; it does not yet address the Planck regime, full quantum-gravity corrections that alter identification of W or Phi, or cosmological horizons. An evidence scoreboard applying a strict referee standard is included as an appendix.