ACORN: Time from Curvature Closure Loops: (Special Theory of Curvature)

Time is used universally in physics, yet its physical origin is rarely addressed. In this paper we show that time is not a primitive quantity, but an emergent measure arising from curvature–action closure. A single invariant proper time T is defined by closed curvature loops. Two equivalent definitions of T arise naturally: one from non-equilibrium (curvature-exchange) mass participation, and one from equilibrium (closure) mass participation. Special and general relativistic time dilation emerge as corollaries describing how approximate coordinate time t relates to T. This construction constitutes the Special Theory of Curvature.