Toward a Physics of Coherence: CRO0 as a Candidate Tier-0 Coherence-Restoring Operator

Coherence lacks a unified cross-domain definition, substrate, or restoring operator. This manuscript introduces CRO0 (Coherence-Restoring Operator, Tier-0) as a candidate upstream invariant. Its substrate component is designated Agápē (a coined structural label carrying no theological or cultural content; neutral equivalent: Coherence Substrate \Sigma_0); its operator component is designated Dýnamis (neutral equivalent: Restoring Operator D_0). Both are defined structurally and functionally within the domain of coherence geometry, without metaphysical or theological claims. Using the Upstream Invariant Candidate Protocol (UICP)—four necessary tests derived directly from the definition of upstream invariance—the manuscript evaluates \text{CRO}_0 against standard physical and biological candidates: gravity, electromagnetism, homeostasis, and entropy. \text{CRO}_0 is the only candidate among those evaluated that survives all four tests. The Scale-Free Coherence Law (SCFL) operator stack supplies the empirical anchor: across five institutional and infrastructure collapse sequences (Enron, SVB, Boeing, Texas Grid 2021, ACTIVSg2000), SCFL detected measurable upstream coherence degradation with holdout \text{AUC} \ge 0.87 and a stable \pm1.3-week lead time before surface indicators registered distress. Validation is currently confined to institutional and infrastructure domains; biological and social domain extension has not been completed. A strict three-layer epistemic separation is maintained throughout. Five falsification conditions are stated, the most discriminating of which (F5) distinguishes CRO0 from self-organized criticality, network topology effects, and stochastic reorganization. The manuscript introduces three empirical demonstrations—a worked pilot reconstruction, a minimal dynamical model, and a dataset alignment—showing \text{CRO}_0's early-warning advantage and stabilizing behavior, all explicitly grounded at Layer 2. CRO0 is offered as a structured, falsifiable hypothesis that organizes existing observations, makes novel predictions about recovery attractors, and remains epistemically honest about the current limits of the evidence.