We present the Topological Density Functional Theory (T-DFT) framework for nuclear decay, a minimal-parameter approach grounded in four analytically derived theorems linking topological field invariants to observables across all primary decay modes. The central topological exponent is Ztopo = Nc Ω2 fG(D=3) σ = 1/2πα ≈ 0.2751, derived analytically from the SU(3) vacuum weight fG(D=3) = 2 (Theorem II, Corollary II-A), the D=3 solid angle Ω2 = 4π, and the topological damping coefficient σ = α/2 (Theorem III). No parameter entering the gauge-group sector is fitted. We validate T-DFT against 698 alpha emitters (ENSDF + NUBASE2020), 7,547 beta transitions (ENSDF, four forbiddenness classes), 738,453 gamma isomers from the full ENSDF database, and 12 drip-line resonances with measured widths. For Z ≥ 83 alpha emitters, the framework achieves ρ = 0.963, R2 = 0.928, RMSE = 1.34 decades with a systematic bias of only +0.09 decades. Beta-decay log ft values are reproduced at RMSE = 1.38 (Allowed, N = 7,167) and RMSE = 1.11 (1st-forbidden, N = 369) with no fitted offsets. A Yang-Mills correction derived from the Casimir operator CA = 3 eliminates the residual bias δ(1U) = −0.055 observed in v2. For gamma isomers, the topological squeezing factor QSQ = exp(−πα) = 0.977335 predicts a universal half-life shift ΔT1/2/T1/2 = 2.3190%, directly testable with HPGe detectors. The drip-line topological floor Texp1/2 ≥ Ttransit is satisfied by all 12 states with measured resonance widths (median over-factor 56.5×). No free parameter is introduced or fitted at any stage; all constants are derived from the gauge-group geometry of the Standard Model.
Luis Rodrigues (Wed,) studied this question.