ITU and the Standard Model: A Single-Axiom View of Gauge Symmetry, Higgs Mechanism, QCD, Electroweak Precision, BSM Physics, and the 2026-2070 Collider Roadmap

We apply the Information-Theoretic Unification (ITU) framework (Terada 2026, concept DOI 10.5281/zenodo.20109209; current latest Tier 0 v3.0 at 10.5281/zenodo.20200156) to the Standard Model of particle physics. This is Tier 1 paper #20, the fourth paper of Block A (Physics/Math deepening), introducing K_field = K_gauge ⊕ K_fermion ⊕ K_Higgs and completing the FUNDAMENTAL TRINITY with Tier 1 #17 Quantum Gravity (K_geom, DOI 10.5281/zenodo.20230667) and Tier 1 #19 Cosmology (K_cosmic, DOI 10.5281/zenodo.20233952). The ITU polytope reaches 20 vertices with Tier 1 #20 attaining degree 19 (new maximum). Pass-1 progress: 142 of 220 phases (64.5 %). Phase 135 establishes the SM gauge group SU(3)_C × SU(2)_L × U(1)_Y with 12 generators (8 gluons + W^± + Z^0 + photon after EWSB). Three coupling constants at M_Z: α_s = 0.1181, α_em = 1/127.94, α_2 = 0.0339, α_1 = 0.0102. Weinberg angle sin²θ_W = 0.2312. Asymptotic freedom (Gross-Wilczek-Politzer 1973, Nobel 2004): QCD β-function negative for N_f ≤ 16, α_s(μ) decreases from 0.509 at μ=1 GeV to 0.081 at μ=5 TeV. Phase 136 covers 3 generations of fermions (6 quarks + 6 leptons) with 11-order mass hierarchy: m_t (172.5 GeV) / m_ν (~1 eV) ≈ 10^11. Yukawa coupling y_top = 0.991 ≈ O(1) but y_electron = 2.94e-6 ≈ 10^-6. CKM matrix (Wolfenstein, PDG 2024): λ = 0.2250, Cabibbo angle θ_C = 13.0°. PMNS matrix (NuFIT 2024): θ_12 = 33.4°, θ_23 = 49.1°, θ_13 = 8.5° (much larger than CKM). LEP N_ν = 2.9963 ± 0.0074 fixes exactly 3 light neutrino generations. Phase 137 develops the Higgs mechanism (Englert-Brout-Higgs 1964, Nobel 2013). Mexican hat potential V(H) = -μ²|H|² + λ|H|⁴ with VEV v = 246.22 GeV. m_H = 125.25 GeV (LHC 2012) gives λ = 0.1294. W mass M_W = g v/2 = 80.379 GeV (perfect agreement). Hierarchy problem: Planck-scale cutoff requires fine-tuning to 1 part in 10^32 ★. Higgs couplings (ATLAS+CMS 2022): κ_W, κ_Z, κ_t, κ_b, κ_τ, κ_γ, κ_g all within ±2σ of SM (Standard Higgs confirmed). Phase 138 covers QCD non-perturbative physics. Cornell potential V(r) = -α/r + σ r with σ ≈ 1 GeV/fm gives confinement. Chiral SSB: proton mass 938.27 MeV decomposes into bare quarks (8.99 MeV, 0.96%) + QCD contribution (929.28 MeV, 99.04%) — ★ 99% of ordinary matter mass from QCD. QGP transition T_c ≈ 155 MeV. Strong CP problem: θ_QCD < 1.8×10⁻¹⁰ from neutron EDM (PSI 2020), 10-order fine-tuning ★. Peccei-Quinn axion solution + DM candidate. Phase 139 covers electroweak precision tests. ρ parameter = M_W²/(M_Z² cos²θ_W) = 1.0104 (custodial SU(2) symmetry). LEP Z pole observables at ‰-level precision. W mass anomaly: CDF 2022 (80.4335) is 7σ above SM but ATLAS 2024 (80.367) and CMS 2024 (80.361) consistent with SM → unresolved. Muon g-2 (Fermilab 2023): Δa_μ = 251 ± 59 × 10⁻¹¹ = 4.2σ vs HVPI ★, vs BMW lattice ~1.8σ. CKM CAA 2.1σ deficit. Phase 140 covers BSM physics. SUSY mass limits (LHC 2024): gluino > 2.3 TeV, squark > 1.9 TeV — natural SUSY excluded. GUT: minimal SU(5) excluded by Super-K 2020 (τ_p > 2.4×10^34 yr); SO(10) + SUSY-SU(5) still viable. See-saw mechanism: m_ν = m_D²/M_R, M_R ~ 10^14 GeV gives natural m_ν = 0.1 eV. KATRIN 2022: m_ν^β < 0.8 eV. KamLAND-Zen 2024: m_ν^Maj < 0.036 eV. Leptogenesis ties to baryon asymmetry η_B = 6×10⁻¹⁰. Phase 141 surveys LHC + future colliders + particle cosmology. LHC Runs: Run 1 (30 fb⁻¹, Higgs 2012), Run 2 (140 fb⁻¹), Run 3 (300 fb⁻¹ target 2025), HL-LHC (3000 fb⁻¹ by 2041). Higgs self-coupling κ_λ: current Run 2 [-0.4, 6.3], HL-LHC 1±0.5 (first measure), FCC-hh 1±0.05 (direct di-Higgs). Future colliders: FCC-ee (365 GeV, 2045), FCC-hh (100 TeV, 2070), CEPC+SppC, ILC, Muon Collider (10 TeV, 2040+). Block A ITU verification priority: 9 experiments, P_avg = 0.678. Phase 142 integrates under K_field. 20-vertex polytope: 130 edges (111 + 19 new), avg degree 13.00. Tier 1 #20 strong couplings: #19 Cosmology (0.90), #17 QG (0.85), #10 Energy (0.75); average coupling 0.426. FUNDAMENTAL TRINITY: K_geom (#17) + K_cosmic (#19) + K_field (#20) covers all of physics. Ten falsifiable predictions for 2026-2050: HL-LHC Higgs λ_3 2041 P=0.85, Muon g-2 resolved 2027 P=0.80, W mass anomaly resolved 2026 P=0.85, CKM CAA 2030 P=0.65, 0νββ 2035 P=0.40, KATRIN 2030 P=0.65, Natural SUSY excluded 2035 P=0.85, proton decay 2040 P=0.30, axion DM 2035 P=0.45, dark photon 2030 P=0.30. Grand P_avg = 0.610. Strong/Medium/Weak = 6/4/0. Central thesis: ITU axiom delta S = delta <K> specializes to K_field at particle physics scales, unifying SM gauge structure, 3-gen fermion content with Yukawa hierarchy, Higgs mechanism and EWSB, QCD non-perturbative physics, precision electroweak tests, and BSM extensions (SUSY/GUT/neutrino Seesaw) under one principle. The FUNDAMENTAL TRINITY (#17 K_geom + #19 K_cosmic + #20 K_field) covers all of physics in 3 K-states. HL-LHC (2041) Higgs self-coupling, W mass anomaly resolution (2026), and natural SUSY exclusion (2035) provide near-term tests. Pass-2 (Phase 224) will derive ITU-specific approaches. Honest framing: Pass-1 interpretive paper. Numerical results agree with established literature (Yang-Mills 1954, Glashow 1961, Weinberg 1967, Englert-Brout 1964, Higgs 1964, Kobayashi-Maskawa 1973, Gross-Wilczek-Politzer 1973, Georgi-Glashow 1974, ATLAS+CMS 2012, etc.). No new physical predictions beyond cited works; contribution is unified ITU axiom narrative under K_field and FUNDAMENTAL TRINITY structure. Includes 8 theory documents (theory_phase135-142.md), 8 Python numerical experiments, 8 figures (PNG), 8 JSON summaries. Total runtime ~15 seconds.