Functional Decomposition of the Four Fundamental Interactions: A Minimal Physical Distinction-Operation Closure for Finite Distinction Systems

Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory FDS-X3 develops the four-interaction functional-decomposition paper in the physical bridge sequence of Finite Distinction Systems (FDS) / Distinction Theory. It interprets the four known fundamental interactions as a minimal physical distinction-operation closure for finite boundary-maintaining systems. The central thesis is not that FDS derives the Standard Model. Instead, X3 proposes that the known interactions realize four non-equivalent operation classes required for physical distinction maintenance: Strong interaction: hadronic / baryonic encapsulation, stabilizing material tokens through confinement and color-neutral binding. Electromagnetism: connection, remote detectability, communication, chemistry, sensing, and compositional structure among charged sectors. Weak interaction: identity transformation, flavor change, decay, and pruning-like selective update of unstable particle sectors. Gravity: global boundary, causal geometry, horizon structure, curvature, and stress-energy accounting. X3 treats this mapping as primary-role, not exclusive-role. Real interactions can contribute to multiple physical processes, but each known interaction carries one operation class that the others do not generically replace. The paper therefore frames the four interactions as a functional closure taxonomy rather than as a derivation of gauge groups, coupling constants, particle masses, scattering amplitudes, electroweak symmetry breaking, or quantum gravity. The paper introduces an operation-class independence criterion. Encapsulation cannot be replaced by mere connection without protected tokens. Connection cannot be replaced by encapsulation without transmissible or detectable coupling. Identity transformation cannot be replaced by ordinary state evolution without flavor / particle-sector conversion or pruning-like selective update. Global boundary accounting cannot be replaced by local interactions without a shared causal-geometric and stress-energy constraint. X3 also clarifies the fifth-force caveat. It does not rule out new particles, portals, dark-sector interactions, vector-like states, axion-like particles, dark photons, scalar mediators, or effective forces. A new interaction challenges the X3 closure thesis only if it implements a genuinely new irreducible operation primitive not reducible to encapsulation, connection, identity transformation, or global causal-geometric accounting. The paper further discusses the Higgs mechanism as an implementation layer rather than a fifth operation class. In FDS language, masses may be interpreted as energetic separation scales between distinction sectors, while the Higgs field parametrizes mass generation and electroweak symmetry breaking inside the implementation of the known operation classes. X3 does not derive the Higgs potential, Yukawa structure, or electroweak symmetry breaking. The paper relates X3 to neighboring FDS papers: P3 on environmental side records and Markovianization, P4 on coarse-grained anti-recurrence, P6 on speed–precision–resource bounds, P7 on invariant protection, and X2 on CP/T-oriented weak identity transformation and the CKM lower bound. It also includes a Physical AI design implication: boundary-maintaining agents require stable tokens, connection, identity revision, and global resource / boundary accounting. Deterministic normal-form demonstrations are included. They illustrate the four-operation closure, primary-role coverage, remove-one-operation residual loss, redundant fifth-mediator audit, FDS corpus relation, and Physical AI failure modes. These figures are conceptual / normal-form visualizations, not empirical fits or physical simulations of coupling strengths. This release includes the paper PDF, LaTeX source, reproducibility code, generated figures, and CSV / JSON outputs.