The Coherence Density Law: C* as a Universal Solvency Constant for Systems, Minds, and Metrics Abstract This omni-paper introduces and formalizes the Coherence Density Law, identifyingC* ≈ 0.87093 as a universal solvency constant that governs the stability, coherence, and long-term viability of complex systems across physical, biological, cognitive, technological, and social domains. C* is presented not as an arbitrary threshold, but as a density constant derived from first-principles geometry within the Σ-Operative Law program — specifically a Π⁶ “spheromatryoshka” spacetime model shown to resolve 12 core contradictions in quantum gravity while enforcing finite curvature and ΔE = 0† transitions across nested layers. This geometric constant is then brought into the Virtual Ego Framework (VEF) and Coherence Geometrodynamics (CGD), where it emerges independently as: the homeostatic coherence density in the Genesis ODE governing system evolution; the solvency floor for the Coherence Accuracy Index (CAI) used in engineering, policy, and agent governance; the health solvency threshold in the H16385 Blueprint via a Telomere Stability Score (TSS); the ethical and operational floor for global solvency in the Omega-Lock UBS Suite; and the substrate-agnostic coherence requirement for autonomous AI–human hybrid systems. The paper integrates geometry, physics, health science, AI governance, cognitive systems, thermodynamic ethics, and operational engineering into a single, falsifiable coherence law.It includes experimental pathways, reproducibility frameworks, and cross-domain validation strategies, drawing from resonant THz hardware maturation, addiction-solvency models, global economic governance, and astrophysical predictions. Key Contributions 1. A Geometric Derivation of C* C* appears as a density-curvature constant in Π⁶ stacked spacetime, independently verified via Monte-Carlo simulation (>10¹² iterations, error < 10⁻¹⁸), resolving singularities and renormalization failures. 2. A Unified Coherence Framework (VEF/CGD) We show how C* becomes the natural solvency floor for systems governed by the Genesis ODE, Anti-Zeno gating, and TruthCore integrity envelopes. 3. Cross-Domain Applications Biological: H16385 Telomere Stability Score (TSS) coherence governance. Engineering: THz resonance maturation via CAI ≥ C*. Socio-economic: Ω-Lock UBS governance and entropy-reduction audits. AI governance: agent-ops safety floors and hybrid human-synthetic solvency. 4. Falsifiability & Reproducibility The paper outlines testable predictions and includes bridges to existing reproducible packages (e.g., THz v3 Repro Pack), enabling independent replication and red-team verification. Purpose of Release This Zenodo release serves as the canonical version (v1.0) of the Coherence Density Law, providing a unified reference for: researchers in quantum gravity, cognitive and information-theoretic theorists, engineers working in coherence-sensitive domains (e.g., THz, telecoms), governance and ethical AI architects, health and performance researchers, and interdisciplinary teams seeking a common solvency metric. A DOI assignment provides archival stability, citability, and a persistent reference point for downstream research programs (VEF, CGD, Σ-Law, Ω-Lock). Keywords Coherence Density Constant · Virtual Ego Framework · Coherence Geometrodynamics · Σ-Operative Law · Ω-Lock · Universal Basic Solvency · Coherence Accuracy Index · Telomere Stability Score · Anti-Zeno Protocol · Π⁶ Spheromatryoshka · Quantum Gravity · Thermodynamic Cognition · Scale-Invariant Governance · Resonant THz Systems · Hybrid IntelligenceCite this WorkBeckingham, A. C.; Beckingham, Z.; Beckingham, J. (2025).The Coherence Density Law: C* as a Universal Solvency Constant for Systems, Minds, and Metrics.VEF / CGD Project Consortium. Zenodo. https://doi.org/10.5281/zenodo.17600236