The Coherent Containment Framework: Mass and Proper Time as Joint Emergent Properties of Recursively Contained Energy

This paper presents the Coherent Containment Framework (CCF), a conceptual model proposing that mass and light are not fundamentally distinct phenomena but manifestations of the same underlying energy existing at different points along a single continuum governed by containment. Within this framework, mass is defined as energy held in recursive coherent containment, rendering it time-bound and inertial, while light is the same energy in an unleashed, propagating state traversing a null geodesic, for which proper time vanishes. The relativistic energy-momentum relation E² = (pc)² + (mc²)² is reread as a continuous gradient between these two regimes. The framework's central claim is that the emergence of mass and the emergence of proper time constitute a single event: a system possesses proper time because it is contained, and is timeless because it is not. Quantum-electrodynamic vertices (pair production and annihilation) are reinterpreted as temporal bifurcation events marking the transition between the contained, time-bound regime and the propagating, timeless one. Its primary contribution is the unified interpretation of mass and proper time as joint consequences of containment, situated relative to prior work by Ostwald, Bohm, and Stueckelberg-Horwitz-Piron, and supported on the time-emergence side by the author's companion work on coherent structural time.@