Einstein, Planck, de Broglie and the Emergence of a Fundamental Closure Time T0 in the ACORN Framework

Einstein’s mass–energy equivalence, Planck’s energy–frequency relation, and de Broglie’s matter–wave hypothesis together point toward a fundamental connection between mass and intrinsic frequency. In the ACORN framework, matter is modelled as closed curvature circulation within a five-dimensional geometric manifold. Quantised loop closure implies the existence of a fundamental recurrence time, denoted T0, such that the product of mass, the square of the invariant propagation speed, and this intrinsic period equals an integer multiple of Planck’s constant. For the minimal eigenclosure state, this reduces to a direct proportionality between rest mass–energy and the inverse of the intrinsic closure time. We show that this relation reproduces the de Broglie rest-frequency expression and identifies T0 with the inverse Compton frequency associated with a stable particle. In this formulation, the familiar mass–frequency relation is not postulated but emerges from geometric closure constraints. Planck’s constant appears as the invariant action accumulated over one complete intrinsic recurrence cycle. The result provides a geometric bridge linking Einstein, Planck, and de Broglie through a single closure principle.