Recursive thermodynamic damping and the closure of spacetime: A bridge between classical and quantum gravity

This study introduces a thermodynamic damping law aimed at regularizing curvature singularities by enabling the self-regulation of spacetime geometry near the Planck scale. The theory predicts a finite curvature resistance that increases as the local radius of curvature decreases, emerging naturally from an entropy-bound condition. This modification of classical general relativity avoids the need for exotic matter or full quantization of gravity. We validate the proposed law across eight distinct astrophysical domains—including black hole ringdowns, pulsar timing arrays, photon ring expansions, neutron star oscillations, gravitational wave echoes, polarization suppression, tidal deformability, and the empirical derivation of π in curved spacetime. A total of 36 independent measurements spanning 18 orders of magnitude yield a combined statistical significance of 7.5σ, surpassing the standard discovery threshold. These results suggest that π is a spectral attractor whose effective value is curvature-dependent, and that recursive damping provides a universal mechanism for embedding thermodynamic memory into classical geometry. The framework offers a falsifiable, observationally grounded bridge between classical and quantum gravity.