The Constant of Time: k = −1 as the Foundational Physical Constant of Gravitation, Relativity, and Quantum Structure

This work introduces the Physical-Time medium (ρt) as a real, measurable field underlying gravitation, spacetime curvature, quantum structure, and cosmic expansion. The constant k = -1 is shown to be the universal coupling representing inward consumption of the ρt field by matter, reproducing classical gravitational behavior while extending seamlessly to quantum and cosmological scales.

Gravitational lensing, orbital precession, time-delay asymmetries, galaxy rotation anomalies, and quasar attenuation are reinterpreted as manifestations of ρt-field compression and replenishment. Empirical correlations are presented using SPARC galaxy rotation curves, COSMOGRAIL time-delay asymmetries, MORX quasar attenuation, and particle-scale harmonic structure. This provides a unified and continuous physical model of spacetime that remains fully compatible with General Relativity while resolving missing-mass and missing-energy anomalies without invoking dark matter or dark energy as separate substances.