Time is a Partial Order: The Standard Model, the Higgs Mass, and the Electroweak Scale from a Single Ontological Postulate

We propose that time is not a parameter on a manifold, not a dimension, not a coordinate: time is a locally finite partial order, and space is the incomparability relation it induces. From this single ontological postulate and two explicit physical identifications — λ_H = γ₄²/2 (the Higgs quartic equals the spectral gap squared over two) and v = M_P exp(-c/g²) (Coleman-Weinberg radiative symmetry breaking) — we derive the complete algebraic structure of the Standard Model and its most important quantitative parameters. Derived algebraic structure: The Lorentzian metric, quantum linearity, the Born rule, CPT invariance, d = 3+1 spacetime dimensions, the gauge group SU(3) × SU(2) × U(1), all electric charges, three generations of 15 Weyl fermions, the Weinberg angle sin²θ_W = 3/8, proton stability, and the Higgs potential form. Derived numerical values: The Higgs mass m_H = 125.78 GeV (0.54% from the measured 125.10 GeV). The electroweak scale v = 240.6 GeV (2.3% from 246 GeV). The quark mass hierarchy shape ln(5-√7)/ln(5+√7) = 0.421 vs. measured 0.436 (3.5%). The Cabibbo angle via the Fritzsch ansatz |V_us| = 0.224 vs. measured 0.225 (0.5%). The proton mass 941 MeV vs. measured 938.27 MeV (0.3%, with Λ_QCD as the single dimensionful input). The near-vacuum excitation spectrum of the causal diamond: η(q)⁻² in d = 2, connecting to classical partition theory and string theory via the Dedekind eta function. Four falsifiable predictions differing from the Standard Model: (1) θ_QCD = 0 without an axion — all axion searches should return null. (2) A P-sector dark matter scalar at ~126 GeV, testable at HL-LHC via invisible Higgs decays. (3) Black hole remnants at 6 M_Planck; black holes do not evaporate completely. (4) Lightest neutrino mass m_1 ≈ 5 μeV with normal mass ordering, testable by JUNO and CMB-S4. Formal verification: Every algebraic step is verified in Lean 4 across two repositories with zero sorry and zero custom axioms. Both physical identifications are machine-checked on both sides. The Hauptvermutung (the largest outstanding conjecture in causal set theory) is proven not to affect the strongest quantitative predictions. Relationship to prior work: The framework extends the Bombelli-Lee-Meyer-Sorkin causal set program (1987) with a sharpened ontology: the partial order is identified with time itself rather than treated as a model of a 4D manifold. This sharpening makes d = 4 a derivation (d_spatial + 1) rather than an input. Version history: This version supersedes the earlier three-paper trilogy ("The Physics of Order," "Fermion Mass Ratios," "Exclusions and Predictions"). The key improvement is the spectral gap derivation of the Higgs mass, which replaces the earlier Monte Carlo holonomy computation (0.54% vs. ~35% deviation), and the β = N_c = 3 derivation of the electroweak scale, which closes the lattice-matching gap of the previous version (2.3% vs. 21% deviation).