Dark-Sector Phenomena as a Geometric Response: A Constitutive Theory of Weak-Field Gravity

This work develops TIDE as a constitutive theory of weak-field gravity. It explores the idea that spacetime geometry may not always track baryonic matter instantaneously, but can relax toward equilibrium over a finite time. In that interval, residual geometry can be read observationally as apparent dark-sector phenomenology.The paper connects this framework across galaxies, lensing, mergers, local flows, and structure formation, using two fixed physical handles: a galactic relaxation clock and an optical projection factor. The result is a compact geometric interpretation of several phenomena usually attributed to dark matter or late-time dark-sector effects.