Evidence of Nuclear-Scale Gravitational Decoherence as a Fundamental Lower Bound for Advanced Interferometric Detectors and Consistency with LISA Pathfinder

The sensitivity of current gravitational wave detectors (LIGO, VIRGO, KAGRA) in the low-frequency band (10-40 Hz) is limited by a persistent noise floor. In this Letter, we propose a phenomenological analysis based on the Diósi-Penrose (DP) model of gravitational decoherence. By treating the spatial cutoff parameter Rc as a free variable and fitting the theoretical displacement noise to the observed LIGO O3 sensitivity limit at 30 Hz, we derive a value of Rc ≈ 2.8 × 10^-15 m. This striking coincidence with the nuclear length scale suggests that semiclassical gravity couples to the discrete nuclear mass distribution. We demonstrate that this model correctly predicts the geometric scaling (1/L) observed between LIGO and VIRGO and, crucially, predicts an identical fundamental noise floor for KAGRA despite its different mirror material (Sapphire) and cryogenic operating temperature (20 K). This implies that the observed limit is material-invariant and represents a fundamental property of spacetime granularity interacting with matter.