The Ukachi Universal Scaling Law: Complete Mathematical Proof and Experimental Validation

This paper presents the complete mathematical derivation and experimental validation of the Ukachi Universal Scaling Law: P =N/πeR4 | log10(M/1 kg)|γ. We providerigorous first-principles derivation from microscopic physics, Bayesian analysis of experimental data, and comprehensive experimental protocols. The derived parametersγ = 6.87±0.15 and N = 2.65×10−34 m4show remarkable agreement with the originalintuitive values of γ = 6.90 and N = 2.78×10−34 m4, achieving 99.6% and 95.3% accuracy respectively. Bayesian model comparison yields Bayes factors > 1000, providingoverwhelming evidence for the Ukachi Law over standard decoherence models.