The Theorems of the Universal Cascade Law: Complete Statement of Results

Description/Abstract: Complete indexed reference for the mathematical results of the Universal Cascade Law (UCL) research program, established across six companion papers (the Math Sextet). Twenty-three theorems, three corollaries, and five testable predictions are presented in a unified numbering system (L1-L23, C1-C3, P1-P5) with theorem statements, source papers, proof status, and DOI references. The results are organized in three parts: Part I (L1-L6) establishes the foundation — the UCL axiom, the geometric derivation of the Feigenbaum constants, the Decay Bounce self-grounding mechanism, the Randolph Constant λᵣ = δ/α = 1.86551077, the four-layer universality hierarchy, and the closed loop within…