Time as a Fundamental Substrate A Conceptual Framework for Pre-Big-Bang Temporal Continuity and Expansion Dynamics

This paper identifies a previously undocumented convergence across three independent mathematical domains — multi-dimensional rotational geometry, black hole horizon mathematics, and cosmic expansion dynamics — each exhibiting identical boundary escalation and discontinuity behavior, suggesting a shared geometric structure that does not depend on matter. Building on this, the paper argues that time is a fundamental substrate predating and outlasting the material universe, with the Big Bang singularity representing the limit of general relativity's model rather than the origin of time itself. A novel experimental methodology is proposed: sound-analog pressure mapping as a primary instrument for locating black holes and mapping unseen mass distribution without direct electromagnetic observation.