Unified Complexity Theory (UCT) v22.0 — One Fixed Point, Two Projections, All Architecture: 206 Constants Across 22 Domains from a Self-Consistent Point on the E₈ Lattice

Unified Complexity Theory (UCT) v22. 0 ONE POINT, TWO PROJECTIONS, ALL ARCHITECTURE Nature does not store its parameters as scattered empirical numbers. It unfolds them from a single discrete-spectral grammar. Ω* is a generative fixed point whose discrete and spectral projections determine the structural constants governing particle physics, cosmology, molecular geometry, and biochemical thermodynamics. Its discrete branch yields 𝒦 = log₂ (4/3) — the unique subcritical drift constant (Terras 1976). Its spectral branch yields π — the lattice Fourier phase (Spectral Charge Theorem). These are not independent inputs but dual projections of one geometric object: Ω* → 𝒦 (discrete) + π (spectral) → E₈, K₁. . . K₈, c, TAX, Δ → ΛCDM, DNA, amino acid thermodynamics, genetic code, neutrino masses, biomolecular energies, structural tables of life. The architecture closes on itself: 𝒦 generates E₈, E₈ produces K-numbers, K-numbers fix the crystallization threshold Nfix = K₇ − K₃ = 114, and Nfix × 𝒦 reconstructs the lattice. Generator equals dissipation. The theory is self-reproducing. FOUR FORCES FROM FOUR NODES Each fundamental interaction arises from a specific node in the E₈ descent — not postulated, but geometrically necessary: • Strong force — K₈ = 240 roots (confinement) • Electromagnetic — K₇ = 126 roots (α⁻¹ = K₇ + K₃ − 1 = 137) • Weak force — K₆ = 72 roots (3 generations from E₆ → SU (3) ³) • Gravity — failed lattice contacts → Sakharov mechanism • Spacetime — K₄ = 24 (D₄ triality, speed of light c = K₈/K₄ = 10) PARTICLE MASSES: ONE LADDER All masses follow the π-Ladder: m = mₑ × (K-prefactor) × πⁿ. • α⁻¹ = 137 (0. 026%, three routes) • mₚ/mₑ = D × K₇ + K₆ = 1836 (0. 008%) • sin²θW = φ/7 (31 ppm) • mW, mZ, mH from K-number combinations • mc = K₃K₇ − K₈ − K₁ = 1270 MeV (exact integer) • Complete CKM: λ = 7/31, |Vcb| = 1/K₄, δCP = π/φ² • Complete PMNS: sin²θ₂₃ = 4/7, sin²θ₁₃ = 2/90 • 11 mesons, 5 baryons, 5 nuclear SEMF coefficients (R² = 0. 972) COSMOLOGY: ONE CORRECTION → THREE OBSERVABLES A single QED vacuum constant Δ = 18/500 enters through mirror symmetry: • Ωm = 1/π − φ/K₈ + Δ/c = 0. 3152 (d = +1) • H₀ = K₆ − K₂/K₁ + Δc = 67. 36 (d = −1) • ln (10¹⁰As) = Dₛp + Δ = 3. 036 (d = 0) Vacuum energy resolved: ρΛ/ρPlanck = π⁻²⁴⁷ where 247 = K₈ + TAX channels. All 24 cosmological parameters within ε. FROM PHYSICS TO LIFE: SAME GRAMMAR The K-number skeleton that governs nuclear binding also determines: • DNA: 85 constants, E = (9/10) (π/2) ⁿ, CG/AT = π²/4 (0. 06%), nucleosome = 146 bp • Genetic code: 20 amino acids = K₈/K₃, 64 codons = K₄ + K₅ • Medicine: heart = K₆ = 72, BP = K₈/K₁ = 120, body T = K₇/c + K₄ = 36. 6°C • Chemistry, geology, oceanography, atmosphere, music, economics 206 constants. 22 domains. 205 within the existence gap ε = 1/114 = 0. 877%. FALSIFIABLE PREDICTIONS 1. r = K₃/TAX⁴ ≈ 0. 005 (CMB-S4 / LiteBIRD) 2. Σmν = 0. 168 eV (KATRIN / DESI) 3. w₀ = −1 exactly (Euclid) 4. 5mC stacking = 2. 221 kcal/mol (calorimetry) 5. Z-DNA shift = +1. 85% (force spectroscopy) VERIFICATION 141 tests, 0 failures, 25 domains, mpmath 50-digit precision. 30 publication figures. Full source code. Results in JSON and CSV. This is an update of UCT v21. 0 (DOI: 10. 5281/zenodo. 19354707).