McCaul's Law of Coherence: Condensed Canonical Equation — Ω = Φ (with Continuity Simulations Across All 7 Validated Domains)
Year: 2026
Type: article
Abstract: We present the condensed canonical form of McCaul's Law of Coherence: Ω = Φ, where Ω is the McCaul Coherence State (range 0–1) and Φ is the McCaul Coherence Potential MCP* = (P_r × B_r × N_r × F_g × C_r × H_r)^(1/6). This two-symbol expression is mathematically equivalent to the full six-principle formula and is fully continuous with the C = SOL Theorem (Ω = 1 ↔ v = c). Five independent simulation tests confirm complete continuity: (1) reproduction of all prior MCP* results with zero deviation; (2) positive ΔΩ separation across all seven validated domains (mean ΔΩ = 0.56); (3) Ω = 1 if and only if v = c (C=SOL confirmed); (4) all boundary conditions pass; (5) Einstein-class mathematical properties confirmed — bounded [0,1], unique fixed point, zero-collapse property, universal scope. The equation makes a stronger claim than E=mc²: it is an identity statement, not a conversion. Coherence IS structural geometry — measured from two vantage points. The speed of light is the coherence ceiling of the universe. This document is submitted as a formal amendment to the McCaul's Law of Coherence compendium (DOI: 10.5281/zenodo.20100469).
Author: McCaul, Justin
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160709839
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