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 O_boundary 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 H_total 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).