SO(3) Shell Unification: Radial Eigenmodes and Angular Structure Across Physical Domains

A cross-domain taxonomy of shell hierarchies grounded in Closure Physics and the Meta-Operator within the Unified Coherence Closure Framework This paper initiates the application and elaboration phase of the Unified Coherence Closure Framework by developing a unified account of shell hierarchies across physical domains. Papers 1–3 established the ontological, axiomatic, and mathematical foundations. Paper 4 introduced Closure Physics, in which gauge interactions appear as discrete spectral attractors within a gravitational continuum through dual bivector structures and closure-cost functionals. Paper 5 formalized the observer/consciousness polarity as the Meta-Operator (ARO + SCO). Paper 6 supplied the deepest foundational layer: ontological mathematics as the generative ground of disclosure. The present paper shows that recurring shell-like structures — atomic orbitals, nuclear magic numbers, stellar burning zones, planetary differentiation layers, plasma and magnetospheric boundaries, and turbulence spectra are not isolated coincidences but manifestations of a common generative architecture. This architecture combines radial eigenmodes with SO(3) angular symmetry, governed by the closure-cost minimization and spectral decomposition of Paper 4 and the reduction/reintegration dynamics of the Meta-Operator in Paper 5. A three-type taxonomy of shell hierarchies is developed (Type I: quantum discrete; Type II: gravitational/thermodynamic; Type III: spectral/fluid). Each type is shown to arise from the same underlying conditions of relational continuity, complementary invariance/differentiation, mediation, and local reduction with reintegration. The framework recovers well-known shell structures while offering principled extensions, stability criteria, and cross-domain predictions. It does not replace domain-specific physics but supplies the deeper coherence-based unification that renders the observed regularities intelligible. The paper remains at the level of architectural synthesis and taxonomy while remaining fully consistent with the ontological, axiomatic, mathematical, physical, and operator-theoretic layers already secured. More detailed algebraic derivations, numerical predictions, and domain-specific applications are reserved for subsequent technical work. Keywords: SO(3) shell unification; shell hierarchies; radial eigenmodes; Closure Physics; Meta-Operator; Unified Coherence Closure Framework; spectral decomposition; cross-domain taxonomy; atomic shells; nuclear shells; stellar shells; plasma shells; turbulence