Finite-Distinction Operation Closure and the Four Fundamental Interactions: Encapsulation, Connection, Identity Update, and Causal-Screen Ledger Geometry

This paper(X3) proposes a finite-distinction operation closure for the four known fundamental interactions. It does not derive the Standard Model gauge group, coupling constants, particle masses, scattering amplitudes, electroweak symmetry breaking, CKM/PMNS parameters, or quantum gravity. Its narrower claim is that any physical world containing finite distinctions that are persistent, communicable, transformable, and globally embedded requires four non-equivalent operation classes: token encapsulation, connection or remote detectability, identity-sector update, and global causal-ledger geometry. In the observed world, the strong, electromagnetic, weak, and gravitational interactions realize these primary roles respectively. The G1 finite-screen gravity program strengthens the fourth row by turning gravity from a loose “global accounting” label into causal-screen ledger geometry: finite causal-screen entropy response, Ward/Bianchi closure, Weyl-normalized residual interfaces, and finite-screen realization prototypes. X3 therefore becomes an operation-closure module in a larger FDS physics spine: X4 supplies matter-address protection, X2 supplies the oriented weak identityupdate module, X3 classifies interaction operation classes, and G1 supplies the global causal-screen ledger. The mapping is primary-role, not exclusive-role. New particles, portals, dark sectors, or fifth-force candidates do not by themselves refute X3; the basis is challenged only by a fundamental interaction implementing a necessary operation primitive not reducible to encapsulation, connection, identity update, or causal-ledger geometry. A visual normal-form layer is included to display operation maps, coverage matrices, remove-one losses, fifth-force audit logic, and relation maps.