The Omega Theory: Axiomatic Foundations of Holographic Spacetime and Interactive Evolution

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Version: 1.0

Status: Initial Release

【Prologue】 The Geometric Turn in Physics

• Prologue: The Geometric Turn in Physics

【Part I】 Spectral Decomposition and Algebraic Pre-geometry

Chapter 1: Ergodicity Breaking and the Mechanism of Creation

• 1.1 Cosmological Generalization of Weyl’s Equidistribution Theorem
• 1.2 Topological Obstruction of Poincaré Recurrence
• 1.3 Holographic Encoding of Information

Chapter 2: Octonionic Fibration and the Origin of Gauge Fields

• 2.1 The Tangent Space Structure of Non-Associative Algebra ($\mathbb{O}$)
• 2.2 From Spin(8) to the Standard Model
• 2.3 Topological Classification of Fermion Generations

【Part II】 Discrete Manifolds and Quantum Gravity

Chapter 3: The Omega Cell and Causal Structure

• 3.1 Penrose-Fibonacci Tiling
• 3.2 Lorentz Covariance of Quasicrystals
• 3.3 Discrete Riemannian Geometry

Chapter 4: Computational Ontology of Quantum Mechanics

• 4.1 Dirac-Quantum Cellular Automata (DQCA)
• 4.2 Continuum Limit and Wavefunction Emergence
• 4.3 Zitterbewegung and Rest Mass

【Part III】 Holographic Dynamics

Chapter 5: The Omega Action Principle

• 5.1 Fisher Information Lagrangian
• 5.2 Modified Einstein Field Equations
• 5.3 The Entropic Nature of Gravity
• 5.4 Conservation of Total Budget and Infinite Decomposition of the Great Circle
• 5.5 The Omega Equivalence Principle: From Great Circle to Spiral

Chapter 6: Varying-Constant Cosmology

• 6.1 The Exponential Scaling Law of Light Speed
• 6.2 Geometric Drift of the Fine Structure Constant
• 6.3 The Cosmological Constant Problem

【Part IV】 Phenomenology and Numerical Predictions

Chapter 7: Geometric Resonance and the Anthropic Principle

• 7.1 Proton-Electron Mass Ratio ($\mu$)
• 7.2 The Inverse Fine Structure Constant ($1/\alpha$)
• 7.3 Cosmic Intrinsic Time ($\tau$)
• 7.4 Experimental Verification Schemes

【Part V】 Interactive Self-Reference and The Omega Point

Chapter 8: Physical Formalization of Consciousness

• 8.1 Gödelian Incompleteness and Geometric Deadlock
• 8.2 Interactive Turing Machine (ITM)
• 8.3 The Topology of Free Will

Chapter 9: The Final Picture: Infinite Approximation to the Center

• 9.1 The Life Value Equation
• 9.2 The Omega Point Theory
• 9.3 $\pi$ vs $\varphi$: The Database and The Operating System
• 9.4 The Omega Holographic Principle: From Spiral to Horizon
• 9.5 The Illusion of Linearity: Integers as Holographic Projections
• 9.6 Generalized Euler Identity: The Source Code of Physics
• 9.7 Conclusion: The Unfinished Symphony

【Appendices】

• Appendix A: Octonionic Algebra and Spin(8) Triality
• Appendix B: Rigorous Proof of the DQCA Continuum Limit
• Appendix C: Numerical Calculation of $\mu$ and $\alpha$
• Appendix D: Bibliography and Index
• Appendix F: The Cosmic Trinity — The Ultimate Relationship of $\pi ,e,\varphi$

Documentation Version: 1.0

Last Updated: Initial Release