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 Kfield = Kgauge ⊕ Kfermion ⊕ KHiggs and completing the FUNDAMENTAL TRINITY with Tier 1 #17 Quantum Gravity (Kgeom, DOI 10. 5281/zenodo. 20230667) and Tier 1 #19 Cosmology (Kcosmic, 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^± + Z⁰ + photon after EWSB). Three coupling constants at MZ: αₛ = 0. 1181, αₑm = 1/127. 94, α₂ = 0. 0339, α₁ = 0. 0102. Weinberg angle sin²θW = 0. 2312. Asymptotic freedom (Gross-Wilczek-Politzer 1973, Nobel 2004): QCD β-function negative for Nf ≤ 16, αₛ (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: mₜ (172. 5 GeV) / m_ν (~1 eV) ≈ 10¹1. Yukawa coupling yₜop = 0. 991 ≈ O (1) but yₑlectron = 2. 94e-6 ≈ 10^-6. CKM matrix (Wolfenstein, PDG 2024): λ = 0. 2250, Cabibbo angle θC = 13. 0°. PMNS matrix (NuFIT 2024): θ₁2 = 33. 4°, θ₂3 = 49. 1°, θ₁3 = 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. mH = 125. 25 GeV (LHC 2012) gives λ = 0. 1294. W mass MW = g v/2 = 80. 379 GeV (perfect agreement). Hierarchy problem: Planck-scale cutoff requires fine-tuning to 1 part in 10³2 ★. Higgs couplings (ATLAS+CMS 2022): κW, κZ, κₜ, κb, κ_τ, κ_γ, κg 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 Tc ≈ 155 MeV. Strong CP problem: θQCD 2. 3 TeV, squark > 1. 9 TeV — natural SUSY excluded. GUT: minimal SU (5) excluded by Super-K 2020 (τₚ > 2. 4×10³4 yr) ; SO (10) + SUSY-SU (5) still viable. See-saw mechanism: m_ν = mD²/MR, MR ~ 10¹4 GeV gives natural m_ν = 0. 1 eV. KATRIN 2022: m_ν^β specializes to Kfield 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 Kgeom + #19 Kcosmic + #20 Kfield) 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 Kfield and FUNDAMENTAL TRINITY structure. Includes 8 theory documents (theoryₚhase135-142. md), 8 Python numerical experiments, 8 figures (PNG), 8 JSON summaries. Total runtime ~15 seconds.