Proxy-Space Regularization of β-Decay Systematics: Recurring Approach Dynamics to Half-Life Minima

This work introduces Sheppard’s Universal Proxy Theory (SUPT), a geometric transformationthat maps β-decay half-lives τ onto normalized coordinates θi = arcsin τmin/τi, where τmin is theminimum half-life within each isotopic chain. Applied to neutron-rich palladium (Pd, Z = 46),cadmium (Cd, Z = 48), tin (Sn, Z = 50), and xenon (Xe, Z = 54) chains, SUPT reveals recurringlinear approach dynamics in θ-space to known τ-minima. Linear regression of θ(N) in pre-minimumregions yields slopes β (degrees/neutron) that show systematic variation with proton number. Thetransformation yields testable predictions with quantified uncertainties for unmeasured isotopes,providing a phenomenological regularization of complex nuclear systematics into a low-dimensionalproxy space for hypothesis generation and experimental targeting.