Closure Theory: From Intrinsic Geometric Closure to Relational Mass, Charge and Coupling

Closure Theory (CT) develops a geometric framework in which matter, mass, charge and interaction are investigated as downstream consequences of completed intrinsic geometry rather than introduced as primitive ingredients. The construction begins from a reduced intrinsic ledger of mass-like, length-like and recurrence-like scales and develops through the Intrinsic Wave Equation (IWE), Canonical Transport Equation (CTE), Canonical Frame Transport Equation (CFTE), FourWay HyperCirc geometry and globally completed intrinsic histories termed Completed Intrinsic Closures (CICs). A central result is the separation of extensive closure multiplicity from intensive oriented structure. Conditional on a globally independent rank-two compact phase base, joint winding gives the topological multiplicity N = |ab| and the corresponding extensive action law J_N = Nh. Reciprocal FourWay winding yields candidate electron and proton passports W_e = (1,1,1,1) and W_p = (17,108,108,17), with candidate multiplicities N_e = 1 and N_p = 1836. Their identification as physical particle sectors remains conditional upon solution of the global Master completion problem. The electromagnetic branch provides a particularly sharp quantitative test. A full-recurrence history balance, cubic intrinsic participation invariant and geometric publication prescription produce Inverse electromagnetic coupling from CT ≃ 137.0442 without using the observed fine-structure constant as an input. Its identification with the observable electromagnetic coupling remains conditional upon completion of the relational publication mechanism. The framework subsequently develops a common relational geometry — the Joint Universal Geometry (JUG) — with complementary orientation-sensitive and orientation-even publication channels as candidate precursors of electromagnetic and gravitational behaviour. Exact cancellation and protected-null structures are obtained, while the absolute gravitational coupling, Maxwell recovery and the general-relativistic limit remain explicit open tests. This work presents the current consolidated formulation of Closure Theory, including its primitive invariants, intrinsic transport and completion architecture, winding topology, completed-action construction, mass and charge publication programme, electromagnetic numerical result, relational geometry and gravitational programme. Particular emphasis is placed on distinguishing derived results, results conditional on stated premises, candidate observable identifications and open problems, thereby making the framework directly testable and falsifiable. Closure Theory is proposed not as a replacement for Special Relativity, Maxwellian electrodynamics or General Relativity in their experimentally established domains, but as an attempt to investigate whether the matter identities and relational sources upon which those theories operate can themselves descend from a more primitive completed geometric structure.