Computational Implementation of Closure-Cost Functionals and Spectral Predictions in Nuclear and Stellar Systems

Initial numerical results and comparison with observational data within the Unified Coherence Closure Framework This paper presents the first computational implementation of the closure-cost functional and spectral decomposition within the Unified Coherence Closure Framework, applied to nuclear and stellar systems. Building on the quantitative predictions developed in Papers 10 and 11 and the synthesis provided in Paper 12, we implement simplified but physically motivated models of the closure-cost functional for nuclear mean-field potentials and stellar structure equations.In the nuclear domain, we compute the locations of shell closures and stability islands by minimizing discretized closure-cost functionals under SO(3) degeneracy and spin-orbit coupling. Initial results recover the known magic numbers and indicate a broad stability region near (N, Z ), consistent with earlier macroscopic-microscopic predictions but derived here from the same variational principles used for gauge-gravity unification. In the stellar domain, we implement the radial + SO(3) architecture for simplified stellar models and compute expected modifications to p-mode and g-mode frequency spacings and damping rates near convective boundaries. The results show characteristic patterns in mode spectra that differ from standard stellar models in testable ways.Initial comparisons with nuclear data tables and helioseismological observations are presented. Parameter sensitivity studies identify the weighting coefficients in the closurecost functional that most strongly influence predictions. The paper concludes with a discussion of computational challenges and a clear roadmap for more detailed numerical work. All computations remain fully consistent with the ontological, axiomatic, mathematical, and operator-theoretic foundations of Papers 1–6 and the predictive architecture of Papers 9–12.