The Universal Regulator: The Universal Coherence Framework and Its Validation

This monograph develops the Universal Coherence Framework, a geometric classificationsystem showing that coherent physical systems—quantum, electromagnetic (across thefull EM ladder from RF to X-ray), optical, mechanical, condensed-matter, gravitational,and cosmic—share a common invariant representation when expressed in terms of threecoherence-relevant scales: a stiffness- or energy-like coordinate M, a geometric coherencecoordinate D, and a coherence timescale τ . Here M represents an effective “coherencestiffness” or energy scale (inertia, curvature-induced acceleration, condensate stiffness,quantum coherence energy, etc.), not necessarily bare mass.Subject to a single-parameter scaling hypothesis, any dimensionally consistent coherencelaw involving these scales and one composite constant κ can be written as a singlepower-law relationMαDβτ γ = κeff ,where the exponent triple (α, β, γ) depends on the dimensional content of κ. In logarithmiccoordinates this relation defines an affine-flat manifold in the (logM, logD, log τ )space, so that, at the structural level, coherence across domains can be analyzed througha unified geometric form.Part I presents the mathematical structure of this classification framework. It introducesthe axioms of coherence, the definitions of the characteristic scales, a dimensionalargument leading to invariant scaling laws for (M,D, τ ) (up to a domain-specific compositeconstant), the proof that the associated invariant manifolds are affine-flat in logcoordinates, an analysis of three levels of geometric universality, and a formulation ofan MDT-Uniqueness Principle stating that, for each coherent system, there is a distinguishedtriple (M,D, τ ) for which static, dynamic, and perturbative coherence are allrepresented by a single planar manifold.A key refinement established in this work is that coherence appears in two universal geometricclasses: a restorative invariant with exponent triple (1,−1, 2) governing optical,electromagnetic, condensate, gravitational, and nonlinear systems, and a diffusive invariantwith exponent triple (0, 1, 1) governing quantum decoherence. Both invariants arisenaturally from the same dimensional-reduction framework in Part I, and together theyprovide a unified coordinate description of coherence across physics.Part II presents the empirical validation. It shows that across a broad collectionof quantum, electromagnetic, optical, mechanical, condensed-matter, gravitational, andcosmological systems, (i) the restorative exponent triple (1,−1, 2) accurately classifiescoherence in all restorative domains (up to trivial rescalings), and (ii) when each systemis expressed in terms of its empirically determined MDT triple, its coherent configurationscollapse onto the corresponding affine-flat surface in the (logM, logD, log τ ) space. Inthis combined sense, the Universal Coherence Framework reveals a shared structuralgeometry underlying coherence across physics, providing a unified classification ratherthan proposing new dynamical laws. Correspondence: ur.coherence@gmail.com