Quantum Criticality as Geometric Singularity: Universal Fidelity Scaling, Temporal Metrics in Discrete Time Crystals, and Experimental Tests of Information-Driven Geometry

We demonstrate that quantum information geometry—specifically the fidelity susceptibility metric on parameter manifolds—exhibits finite-size scaling and curvature singularities at quantum critical points that are structurally identical to geometric response equations, and we propose that Floquet discrete time crystals (DTCs) extend this framework to include temporal metric components whose divergence at DTC melting transitions can be experimentally tested as a probe of emergent spacetime structure in driven quantum matter.