GTE Coordinates as Nuclear Descriptors

We show that GTE (Generative Triple Evolution) coordinates derived from nucleon-triple compositions provide competitive predictive power for nuclear binding energies. In a controlled ablation against equal-size baselines—both using exactly 50 features—GTE composition features achieve a 10-fold cross-validated MAE of versus for equal-size random polynomial features (same dimensionality) and for enriched Bethe-Weizsäcker features. The $ \!25 The paper also presents 6-term analytical laws derived from GTE coordinate features, achieving /A MAE for binding energy. For nuclear stability, the parsimonious 6-term logistic law achieves in 5-fold cross-validation (majority-class baseline: 75.0 Additionally, we present an independent analytical derivation of all seven nuclear magic numbers \2, 8, 20, 28, 50, 82, 126 from the GTE cascade. The Nilsson spin-orbit coupling is derived from one-pion-exchange physics, with f_ and m_ predicted by the GTE cascade (P01–P02), giving _ GTE 0.050 at A = 50 after a standard nuclear many-body suppression factor F_ SR 0.42. With a tensor-force correction from the same pion-exchange parameters, all seven known magic numbers appear as large energy gaps in the single-particle spectrum. This constitutes an order-of-magnitude derivation of the shell-closure structure from GTE (bridge claim, ). Furthermore, the ratio _ emp/ _ min(N=50) = 1.149 IPT = 1.1309 (Information Profit Threshold, $1.6 Scope note: The main ML and analytical-law results demonstrate GTE coordinates as a competitive feature space for nuclear structure. The magic-number derivation is an independent analytical result; it uses one nuclear many-body input (F_ SR 0.42) not independently derived from GTE, and the tensor-force correction should be verified with a full shell-model computation. Predictions beyond the training domain (Z>118) are explicitly speculative (Category D).