Relational Actualism and the Standard Model

Relational Actualism (RA) grounds physics in a single ontological commitment: that irreversible on-shell actualization events, writing permanent directed edges into a growing causal Directed Acyclic Graph (DAG), are the primitive physical reality. The companion papers in this suite have shown that quantum mechanics is exact at the discrete level, that special-relativistic kinematics follow from integer counting (c = lP/tP, E = γ mc²), and that general relativity is the unique consistent macroscopic description of the DAG, via BDG uniqueness (Benincasa-Dowker 2010) and confirmed independently by Lovelock's theorem, given the Lean-verified conservation and covariance results. This paper extends the program to the Standard Model. We propose that the Benincasa-Dowker-Glaser (BDG) local topology of a 4D causal graph has exactly four independent integer-valued degrees of freedom (N₁, N₂, N₃, N₄), one of which is already used by gravity. The remaining three give exactly the three non-gravitational gauge interactions: electromagnetism (U (1) ), the weak force (SU (2) ), and the strong force (SU (3) ). From this single structural observation we derive: electric charge quantization in units of e/3 (three spatial dimensions plus the Lean-verified LLC) ; photon masslessness (zero net BDG debt per cycle) ; topological colour confinement and exact baryon number conservation (LLC on N₂ spatial winding) ; maximal parity violation as a theorem (DAG acyclicity plus retarded BDG action) ; all three force ranges from BDG cost and LLC balance; Regge trajectories; exactly three generations and no fourth (N₅ absent in 4D BDG) ; the Koide lepton mass formula from SU (3) gen symmetry, with scale m₀ ≈ mₚ/3 to 0. 35%; neutrino oscillations from actualization frequency differences; grand unification as the Planck-scale limit of SU (3) colour × SU (3) gen giving ²θW = 3/8; and the gauge coupling hierarchy from BDG coefficient magnitudes. Specific predictions: lightest neutrino mass m₁ ≈ 0. 37 meV, m_ν ≈ 59 meV (testable with CMB-S4/Euclid), and no proton decay (exact baryon conservation). Supersymmetry is structurally absent. Three derivation targets were originally scoped; Derivation 1 (stable pattern enumeration) is now closed by the companion paper RATM, which provides a complete Lean-verified proof (D1closurecomplete, 124 extension cases). Derivation 3 (coupling constants) is substantially resolved: αEM^-1 = 137. 036 via the discrete Dyson equation and αₛ = 1/√72 from BDG integers alone. Derivation 2 (fermion mass chain) remains the primary open target. New result: αEM^-1 = 137. 036 is derived via the discrete Dyson equation from BDG integers alone, matching the PDG value to 0. 00001% with no free parameters. The per-link actualization probability is identified with the fine structure constant pₜh = αEM via the optical theorem, removing pₜh as a free parameter. Additional consequences: θQCD = 0 exactly (strong CP dissolved; no axion needed) ; the black hole information paradox dissolved via Causal Severance partition; and the baryon asymmetry as a Causal Severance initial condition. A companion paper, Relational Actualism: The Topology of Matter (RATM), extends the BDG particle classification to a complete Lean-verified proof: the BDG-stable causal topology types in 4D form a five-element closed set (isolated, depth-2 chain, depth-4 chain, symmetric Y-join, asymmetric Y-join), partitioned into sequential types (leptons and gauge bosons, propagating freely) and topological types (quarks and gluons, confined). Confinement is proved as a theorem---not postulated---with finite BDG-filtration lengths L=3 (gluon) and L=4 (quark). The closure theorem (all extensions of all particle types land within the known set, exhaustively verified over 124 extension cases) establishes that the BDG particle universe admits no new elementary topology types. All algebraic claims in this paper are independently verified: a Python verification notebook confirms 52/52 numerical checks (algebraic identities over 1000 test angles at machine precision 10^-14; hybrid conjectures against PDG 2022 inputs). Two Lean 4 proof files, totalling 176 results across eight files with one intentional sorry (the LQI adapter) and no new axioms, verify: the SU (3) gen coherent state lemma φ_θ (n=1) = (√6/2) e^-iθ; the complete BDG particle classification (D1a--D1h) ; colour confinement; the particle universe closure theorem; Gell-Mann--Nishijima consistency for all six first-generation fermions; and 70 further results.