McCaul's Law of Coherence: A Unified Cross-Domain Compendium — Coherence as a Universal Physical Invariant from Fluid Dynamics to Quantum Systems, Plasma Optics, Biological Signaling, and the Geometry of Light

This compendium presents the complete corpus of McCaul's Law of Coherence — from theoretical foundations through empirical validation across seven independent datasets, physical instrument confirmation, quantum extension, and cosmological implications. The central quantity, the McCaul Coherence Potential (MCP*), is defined as the geometric mean of six physical principles: Phase Regularity (P_r), Boundary Continuity (B_r), Noise Resistance (N_r), Field Geometry (F_g), Coupling Ratio (C_r), and Harmonic Resonance (H_r), with universal threshold θc = 0.25. Cross-domain validation (7 datasets, 6 domains, zero threshold retuning): Ground-penetrating radar: Cohen's d = 1.87, AUROC = 0.800 Underwater sonar: Cohen's d = 10.03, AUROC = 1.000 3D LiDAR point clouds: Cohen's d = 153.42, AUROC = 1.000 BOS/Schlieren fluid dynamics Re=11,300: Cohen's d = 7.74, AUROC = 1.000 BOS/Schlieren fluid dynamics Re=5,890: Cohen's d = 7.65, AUROC = 1.000 (Reynolds invariance confirmed) Plasma optical emission spectroscopy: Cohen's d = 1.61, AUROC = 0.882 Biological calcium wave (C. elegans oocyte): Cohen's d = 319.26, AUROC = 1.000 Physical instrument confirmation: Hybrid RF-Electric Plasma / Structured Optics System — Cohen's d = 2.28, AUROC = 0.947, p < 10⁻¹³². Theoretical extensions: Hydrogen orbital simulation: 1s ground state scores MCP* = 1.0000; rank-order fidelity perfect Primordial nucleosynthesis: SOL geometry with H₂O achieves MCP* = 0.5028 at 300K Quantum extension: 7th State requires N_r ≥ θc^(1/6) = 0.7937 (no free parameters) C=SOL Theorem: c is the unique velocity at which MCP*(vacuum) = 1.0; four corollaries derived Zinc spark at fertilization: biological 7th State threshold crossing with three testable predictions Preregistration timestamp: 2026-05-08T15:35:31.542059Z (SHA-256 verified, unchanged)