The "Matter" of Emergence

Abstract We present a mechanical framework for emergence that replaces origin narratives with persistence criteria. The central claim is minimal: structure emerges when retention mechanisms dominate loss mechanisms over the timescale that matters. This principle is formalized through a dimensionless selection number S = R/(Ṙ·t_ref), where R measures retained structure, Ṙ measures loss rate, and t_ref defines the relevant persistence horizon. Emergence proceeds through staged constraint acquisition within what we term the Collapse Tension Substrate (CTS): scalar variation (0D) → directional bias via gradients (1D) → recursive memory via circulation (2D) → boundary closure via curvature lock (3D). Each stage…