Conventional nuclear models, from liquid-drop parametrizations to shell and density-functional theories, describe many global trends in binding and decay but remain probabilistic and heavily parameterized. They do not explain, from first principles, persistent anomalies such as deep sub-barrier fusion hindrance, odd-even staggering in fission yields, or the long half-life of 14C. This work extends Trembling Spacetime Relativity Theory (TSRT) into the nuclear domain as a deterministic geometric framework for structure, stability, and transformation. In TSRT, each nucleus is a localized trembling-curvature eigenmode whose stability results from sustained suppression of intrinsic spacetime curvature. Decay is a causal relaxation of this suppression and is modeled as curvature reconfiguration rather than a stochastic transition. Binding, fission, fusion, and decay thus emerge from the same geometric dynamics. Using a single global normalization fixed once on 60Co, the TSRT formulation reproduces experimental half-lives across beta decay, alpha decay, and spontaneous fission over more than twenty orders of magnitude, with a mean logarithmic deviation below one part in a million. No shell closures, pairing corrections, empirical preformation factors, or per-nucleus tuning are invoked. The 14C anomaly follows from its geometric beta-path curvature without adjustable hindrance. All Q-values, barrier actions, and emission rates follow deterministically from the spacetime metric and its curvature energy, and TSRT provides a causal mechanism for mass–energy conversion as curvature redistribution. TSRT also reproduces the emergence of neutron magic numbers as geometric minima of the curvature–stiffness map, matching the conventional magic sequence without quantum postulates. Deep sub-barrier fusion hindrance arises from geometric suppression of trembling-mode overlap; odd-even staggering in fission yields originates from phase-locked neck eigenmodes at scission; and electron-screening shifts reflect renormalization of near-field electromagnetic curvature. These effects are consistent with the trembling-spacetime geometry that also underlies atomic structure, photon emission, and gravitational redshift. Quantitatively, TSRT reproduces absolute nuclear half-lives from milliseconds up to about ten quintillion years, with mean logarithmic deviation below one millionth, using only three global constants fixed once per mode. This accuracy surpasses conventional microscopic and empirical models—which typically yield mean logarithmic deviations between one tenth and one hundredth—by roughly ten thousand times, showing that nuclear decay is a deterministic geometric phenomenon rather than a stochastic process. All physical quantities are expressed in absolute SI and nuclear units, with TSRT calibration constants tied to fundamental curvature and lifetime anchors without empirical scaling. TSRT also reproduces absolute fission energetics, yielding a total energy release of 170.0 MeV for thermal-neutron-induced U-235 (n,f) without any per-observable tuning. By deriving nuclear binding, decay, reaction timescales, and mass–energy conversion from a single geometric principle, TSRT establishes a unified, predictive, and reproducible description of nuclear stability and transformation. It bridges microscopic nuclear structure with macroscopic relativistic consistency, showing that mass–energy balance and decay kinetics are natural manifestations of curvature redistribution in trembling spacetime.