Unified Complexity Theory (UCT) v21. 0 — Complete Dynamics Edition This monograph demonstrates that all fundamental physical constants — including the fine structure constant (α⁻¹ = 137), the proton-to-electron mass ratio (mₚ/mₑ = 1836), nuclear binding energies of 3, 554 nuclei, and the Einstein field equations — are geometric necessities of the E₈ root lattice, derived from two algebraically independent irrational seeds with zero free parameters. TWO SEEDS: • 𝒦 = log₂ (4/3) generates STRUCTURE: kissing numbers K₁–K₈, K₂₄, particle counts, coupling constants • π generates CURVATURE: loop corrections, binding energy, geometric phases Every physical constant = 𝒦-integer + π-correction (Theorem S-18, Universal Projection Law), interface precision ≤ 0. 08%. KEY RESULTS OF v21. 0: 1. α⁻¹ = 137 — dynamical derivation. E₈ → E₇ × U (1) branching yields bare coupling α₀⁻¹ = K₇ = 126 (unique among all 8 Dynkin nodes). One-loop vacuum polarization with K₃ − 1 = 11 channels: IUCT = 12. 959 vs Rothe (2012) I = 12. 99 (0. 24% match). Error vs experiment: 0. 026%. 2. mₚ/mₑ = 1836 — dynamical derivation. D × K₇ + K₆ = 14 × 126 + 72 = 1836 (error 0. 008%). Uniqueness: scanning ALL D×Kᵢ+Kⱼ, only this matches. Cross-check: 6π⁵ = 1836. 118. 3. Nuclear binding energy — 3, 554 nuclei. All 5 Weizsäcker SEMF coefficients from kissing numbers, zero fitting. Pairing aP = K₃ = 12 MeV (exact). AME2020: R² = 0. 972 (A ≥ 20), mean error 0. 54%. Actinides: R² = 0. 999. 4. Emergent general relativity. Hopping tensor A^μν (x) on E₈ lattice → effective metric → Einstein-Hilbert action → Sakharov mechanism → G_μν + Λg_μν = 8πG T_μν. Nₑff = 700. Cosmological constant: ρ_Λ/ρPlanck = π⁻²⁴⁷ = 10⁻¹²²·⁸ (obs: 10⁻¹²², match 0. 7%). 5. Self-containment. Nf = 3, ΣQ² = 8/3, 𝒦 itself — all derived from E₈ via four uniqueness proofs. Zero adjustable parameters. WHAT'S NEW vs v18. 5: • Dynamical derivation of α⁻¹ = 137 and mₚ/mₑ = 1836 (was: K-number identities) • Self-containment proved (four uniqueness proofs) • Universal Projection Law (Theorem S-18: Two Seeds) • D = 14 proved by exhaustive scan D = 2. . 30 • All Layer 2 hypotheses → Layer 1 (proved) or Layer 3 (analogy) • Pulsar glitch verification: 2870 ATNF pulsars, z = 10. 7σ • 18 Structural Theorems, Six Constraint Ladders (42/42 checks) • 280 total production checks at 150-digit precision FALSIFIABLE PREDICTIONS: 1. Magic number 184: Fl-298 (Z=114, N=184) on island of stability (GSI/JINR) 2. Lattice Lorentz violation: ΔE/E ~ (E/EP) ² × 48 (gamma-ray burst timing) 3. Neutron star EOS stiffening at ρ₀/2 (LIGO/Virgo) 4. 20 amino acids as geometric necessity (Europa Clipper) VERIFICATION: Production Python code included (UCTᵥ21Production. py). 145 checks, 100% passed, mpmath 150-digit precision. Lean 4 formalization of Collatz: 215 theorems, 0 sorry. CLAIM REGISTER: 81 classified claims — 31 theorems, 14 certified, 13 tier-0, 7 tier-1, 6 tier-2, 5 tier-3, 2 predictions, 2 speculative, 3 analogies. Three-Layer Honesty Audit in Appendix K. This is an update of UCT v18. 5 (DOI: 10. 5281/zenodo. 18355981).
Aleksei Novgorodtsev (Tue,) studied this question.