Formal Foundations of the Concentric Orbital Cosmological Model: Axiomatic Structure, Theorem Chain, and Derivation of the Inter-Ring Coupling Operator from p-Brane DBI Action

Paper 4 and formal foundation of the COCM tetralogy. Establishes six axioms, derives the inter-ring coupling operator Oboundary from the DBI action of the focal p-brane C0, proves its Hermiticity, and establishes a nine-theorem chain from the axiom set to the master equation. Resolves the central limitation of Paper 3. Companion to DOI: 10. 5281/zenodo. 19950582, 10. 5281/zenodo. 19991607, and 10. 5281/zenodo. 20090596. Version 2. 0 adds a formal discussion of the relationship between the COCM enlarged Hilbert space Hₜotal and the covariant Hilbert space framework of Nomura, Varela and Weinberg (2013) in Section 9. 2, and adds reference 26: Nomura et al. , Physical Review D, 87 (8), 084050 (2013).