Floquet time crystal sensor reaches 95% of Heisenberg limit with parity observable in NMR testbed

The study models a periodically driven spin chain as an FTC sensor and derives that the SLD operator, while saturating QFI, can be replaced by local parity measurements for certain initial states. In numerical simulations matching state-of-the-art NMR coherence times and drive strengths, the method-of-moments estimator with parity recovered 95% of the QFI bound for ac fields near 1 kHz. This bridges abstract quantum metrology bounds to hardware constraints where full SLD implementation remains infeasible. Prior NMR time-crystal work (Nature 2021, Choi et al.) demonstrated DTC order but lacked metrological optimization; the new analysis quantifies how DTC rigidity directly reduces back-action noise in sensing protocols. Crossovers to atomic-clock navigation and axion searches become realistic once parity readout is integrated with existing NV or superconducting platforms. The central limitation remains the assumption of perfect periodic driving; Floquet heating at higher drive amplitudes will degrade the approximation. A 50-spin trapped-ion demonstration with calibrated decoherence would strengthen claims for deployable sensors.