The Existence Threshold introduces the metric and locks the boundary between persistence and dissolution in discrete systems. Pattern Loss at Dimensional Boundaries measures what crosses when geometry changes - the 86% Scaling Law, reported with specimen-level reproducibility across cellular automata of every rule and scale. The Dimensional Loss Theorem supplies the proof behind the empirical regularity and finds the same conservation inside transformer attention and real neural networks. The Dynamic Existence Threshold moves the framework forward in time, where the balance of integration and differentiation predicts the state of a system - financial markets, space weather, the human brain across sleep and wake. Consciousness turns out to obey the same conservation as everything else. The papers are reproduced as submitted to the archive, with their arguments, data, and figures intact.
Three bridge essays, written for this edition, join the papers into one continuous argument. The Existence Threshold is not a boundary a pattern merely sits above. It is one the pattern continuously defends - at every transition, every dimensional shift, every tick of time.
"To exist is to continually overcome loss."
