We present the Topological Density Functional Theory (T-DFT) framework for nuclear decay, grounded in four analytically derived theorems that link topological field invariants of the SU(3) vacuum to observables across all primary decay modes. The central topological exponent is Ztopo = Nc Ω2 f(D=3) G σ = 12πα ≈ 0.2751, derived analytically from Nc = 3, the D=3 solid angle Ω2 = 4π, the SU(3) vacuum weight f(D=3) G = 2 (Theorem II, Corollary II-A), and the topological damping coefficient σ = α/2 (Theorem III). No parameter entering the gauge-group sector is fitted; all gauge-sector constants are algebraic invariants of the Standard Model. The nuclear-structure sector introduces a small number of classical boundary conditions fixed by nuclear matter data, not by optimization against decay lifetimes; these are enumerated explicitly in Sec. IIC. We validate T-DFT against 698 alpha emitters (ENSDF + NUBASE2020), 7,547 beta transitions across four forbiddenness classes, 738,453 gamma isomers, and 12 drip-line resonances. For Z ≥ 83 alpha emitters the framework achieves ρ = 0.963, R2 = 0.928, RMSE = 1.34 decades with a systematic bias of +0.09 decades. Beta-decay log ft values are reproduced at RMSE = 1.38 (Allowed) and RMSE = 1.11 (1st-forbidden) 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. The electromagnetic squeezing factor QSQ = exp(−πα) = 0.977335, derived from the U(1) sector of the T-DFT functional measure, predicts a universal half-life shift ΔT1/2/T1/2 = 2.3190%, directly testable with HPGe detectors. The drip-line topological floor is satisfied by all 12 states (median over-factor 56.5×).
Luis Rodrigues (Wed,) studied this question.