We formalize an exploratory geometric Effective Field Theory (EFT) utilizing an Einstein-Cartan-Sciama-Kibble (ECSK) action, where the vacuum undergoes a phase transition governed by a scalarfield coupled to the trace of the stress-energy tensor. To avoid ghost instabilities, we map thenon-minimal coupling to the Einstein frame and stabilize the high-density limit with a quartic po-tential. Relaxing the uniform-spin approximation, we parameterize finite-nucleus spin gradients viadimension-6 EFT Wilson coefficients set by the nucleon mass scale. We compute the 1-loop spinorself-energy using Pauli-Villars regularization matched to the electroweak scale (246 GeV). Utilizingmacroscopic storage ring densities, we demonstrate the ECSK contribution to the muon anoma-lous magnetic moment is kinematically suppressed to O(10−42) even under maximal ensemble spinalignment, explicitly verifying Standard Model dominance. We establish tree-level CPT invariance,noting that loop-level CP phases require future Renormalization Group Equation (RGE) flow anal-ysis. We extract order-of-magnitude upper bounds on geometric elasticity using Calcium isotopeshifts, deriving the sensitivity gradient while accounting for PREX/CREX systematics. Finally,we provide a falsifiable null-hypothesis test for the 2p to 1s X-ray lineshape shift in Kaonic hydro-gen, acknowledging that covariant QCD subtractions from optical potentials strongly correlate withgeometric compression, necessitating future hadronic background improvements.Keywords: ECSK Theory, Spacetime Torsion, Metric Deformation, Kaonic Atoms, J-PARC, Effective Field Theory.