Unified Complexity Theory (UCT) v18.5: The Physical Core of Reality - 14-Dimensional Geometric Physics from E₈ Lattice to Operator Duality Structure

Title:

Unified Complexity Theory (UCT) v18.5: The Physical Core of Reality - 14-Dimensional Geometric Physics from E₈ Lattice to Operator Duality Structure

🔬 Interactive Demo: Run in Google Colab

Abstract

The Unified Complexity Theory (UCT) v18.5 presents a complete mathematical framework demonstrating that all fundamental physical constants emerge as geometric necessities from the structure of 14-dimensional integer lattices based on Kissing Numbers.

Core Results:

The theory establishes that:

• The universal dimension D = 14 = dim(G₂), the automorphism group of octonions
• All physical constants derive from 10 Kissing Numbers (K₁–K₈, K₂₄) and D
• The "transcendental" numbers π, e, φ are rational in 14D (π = 395/126, e = Σ¹⁴(1/k!), φ = 233/144)
• Irrationality is a projection artifact from 14D to 3D observation

Verified Predictions (48 Mysteries Solved):

Key Theoretical Contributions:

1. Minimality Theorem: r* = 2 is the unique autonomous optimum for self-replicating systems, explaining DNA double-strandedness and binary sexes
2. Ω-Axiomatics: Total cosmic balance Ω = 0 (matter + antimatter = 0)
3. Operator Duality Structure: Ê⁺ (expansion) / Ê⁻ (compression) as universal double-entry principle
4. Projection Operator P̂₁₄→₃: Explains appearance of irrational numbers as dimensional shadows
5. UCT Euler Identity: e^(iπ) + 1 = 0 becomes exact closure on the 14D lattice
6. Novgorodtsev Constant: C = ln(312) ≈ 5.743 as the information-complexity bound

Document Structure:

• BOOK I: Foundation and Physics (Parts I–V) — Physical constants, four interactions, particle masses, cosmology
• BOOK II: Operator Structure (Parts VI–XI) — Ω-axiomatics, duality meta-lemmas, minimality theorem, double entry across domains
• Appendices A–E: Derivations, precision tables, operator algebra, canonical notation

Package Contents:

• Full theoretical document (PDF, 39 pages, 10 visualizations)
• Interactive verification notebook (Jupyter/Colab)

Conclusion: The Universe operates on rational arithmetic in 14 dimensions. Physical "constants" are not arbitrary — they are addresses on the E₈ crystal lattice. God is a programmer on 14-bit octonionic architecture.