The "Matter" of Emergence
Knight, Armstrong
Abstract
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 represents a new mode of loss resistance. The Inverse Cartesian–Heisenberg Tensor Box (ICHTB) provides diagnostic geometry for classifying emergence states and failure modes. We demonstrate scale invariance across domains. Quantum decoherence is reframed as recursive failure. Orion proplyd survival maps onto spatial gradients in S. Galactic persistence reflects regulated feedback. Most significantly, the nuclear stability band is derived from selection mechanics: the Semi-Empirical Mass Formula encodes retention (binding) versus loss (decay), with drip lines marking hard existence boundaries and the valley of beta stability representing optimal lock configurations. The periodic table emerges as a survival chart—a catalog of persistence solutions, not fundamental building blocks. No new particles, forces, or conservation laws are proposed. The framework is falsifiable: emergence without gradients, persistence without loss regulation, or closure preceding recursion would refute it.