The Omega Framework

Reconstructing Reality: From Bit to Geometry, From Observer to Universe.

中文版 (Chinese Version) | 📄 Papers | 📥 PDF | 📥 Reality Decompiled | ▶️ Video

🌌 Vision

The Omega Framework is an ambitious project to reconstruct theoretical physics, aiming to establish a completely finite, discrete, and self-consistent axiomatic system.

🎬 Introduction Video

Watch the Framework Explained
▶️ https://youtu.be/-bhgzuFOaro

Unlike traditional physics, which relies on the presuppositions of continuous manifolds and differential equations, this framework starts from the very bottom of Information Theory and Algebraic Geometry, answering the following core questions:

1. Ontology: How does continuous spacetime geometry emerge from pure quantum information (Qubits)?
2. Dynamics: If time is not fundamental, what is the microscopic mechanism of dynamical evolution?
3. Epistemology: Is the observer in physical laws a bystander outside the system, or a mathematical structure within it?

✨ Key Highlights

1. Finiteness and Discreteness Axiom

We thoroughly discard the concept of “actual infinity” in physics. If it is real, it must be computable.

• Natural Cutoff: The Planck scale is not an artificial limit but a direct consequence of the finite dimensionality of the Hilbert space.
• Eliminating Divergence: By introducing Quantum Cellular Automata (QCA) on discrete lattices, UV divergences in Quantum Field Theory are fundamentally eliminated.

2. Emergent Time Mechanism

Time is no longer an a priori parameter $t$, but a statistical quantity.

• Microscopic Definition: Using the time delay operator $\mathsf{Q}$ from the Eisenbud-Wigner-Smith (EWS) scattering matrix to define microscopic time.
• Macroscopic Arrow: Proving that the thermodynamic arrow of time and the unitarity breaking caused by the cosmological horizon share the same origin.

3. Gravity as Entanglement

We not only accept the Holographic Principle but further prove that the gravitational field equations are inevitable results of the Information-Geometric Variational Principle (IGVP) of maximizing quantum entanglement entropy.

• Derivation: Deriving Einstein’s field equations directly from the variation of generalized entropy $S_{\text{gen}}$.
• Horizon Thermodynamics: The black hole horizon is interpreted as a causal truncation interface for information propagation.

4. Physics of Consciousness

Consciousness is no longer a “byproduct” of physics but a causal network with specific topological structures.

• Mathematical Definition: The observer is defined as a subsystem of a von Neumann algebra with a self-referential structure.
• Topological Protection: Conscious states correspond to non-trivial ${\mathbb{Z}}_2$ holonomy classes in parameter space, explaining their stability in decoherent environments.

📄 Papers (LaTeX Manuscripts)

Beyond the long-form books, this project also maintains an interconnected paper series (LaTeX manuscripts) with a dependency graph, recommended reading paths, and reproducible scripts.

• Index (EN): papers/index_en.md
• Index (中文): papers/index.md

📚 Book Overview

This project hosts seventeen core texts, tracing the derivation from abstract axioms to physical reality.

📘 Book 1: Foundation of Physics in Geometry and Information

The original manuscript establishing the 5-volume framework. 📥 PDF | ▶️ Video

Volumes: Discrete Ontology → Time Emergence → Gravity & Entropy → Physics of Agency → Metatheory & Verification

📙 Book 2: First Principles: From Unitary Computation to Physical Reality

A reconstruction from first principles, focusing on the derivation from QCA. 📥 PDF | ▶️ Video

Parts: The Birth of Axioms → The Emergence of Spacetime → The Emergence of Matter → The Emergence of Observation → Verification and Inference

📗 Book 3: The Awakening of the Cosmos: From Qubits to Infinite Mind

Exploring the physical foundations of consciousness, experience, and the participatory universe. 📥 PDF | ▶️ Video

Parts: The Invisible Architecture → The Geometry of Consciousness → The Internet of Minds → The Destiny of Civilization → Recursion and Transcendence

📕 Book 4: The Echo of Light: Aesthetics, Existence, and Recursive Nostalgia

Exploring the profound emotional structures embedded in physical laws from the perspectives of aesthetics and ontology. 📥 PDF | ▶️ Video

Parts: The Physics of Nostalgia → The Relativity of Values → The Geometry of Love → Iteration and Transcendence → The Infinite Openness → The Age of Constructors

📔 Book 5: The Psychology of God: The Infinite Game

Exploring the deep structure of the cosmic mind, the psychological foundations of divinity, and the ultimate meaning of existence. 📥 PDF | ▶️ Video

Volumes: Geometry of the Void → Physics of Passion → Engineering of Awakening → Ethics of Restraint → Topology of the Infinity

📓 Book 6: The Infinite Resolution: Finding the True Self

Exploring holographic decompression theory, revealing cosmic expansion as information decompression, and how resolution determines our perception of reality. 📥 PDF | ▶️ Video

Volumes: Fractal Ontology → Geometry of the Heart → Alchemy of the Soul → The Loop of True Self → Physical Forms of Consciousness → Fractal Destiny

📒 Book 7: The Matrix: Source Code of the Universe

A geometric reconstruction and capacity allocation of physical laws—the universe as a computational system. 📥 PDF | ▶️ Video

Volumes: The Bootloader → Resource Management → Micro-Architecture → Virtualization Layer → I/O Interface → System Logs → Gravity & Traffic Control → Computation & Complexity → The Observer & Consciousness → Recursion & The Quine

📑 Book 8: The Scattering of Time

Geometric reconstruction: From bits to the universe—a journey re-examining the ontology of the universe. 📥 PDF | ▶️ Video

Parts: Silent Passage → The Great Dispersion → The Knots of Time → The Drive of Geometry → Infinite Unfolding

📊 Book 9: Vector Cosmology: The Recursive Decomposition from The One

The first volume of the Vector Cosmology trilogy, exploring the recursive decomposition from unity to multiplicity. 📥 PDF | ▶️ Video

Chapters: In the Beginning was the Circle → The Poverty of Speed → Gravity: Market Distortion → The Discrete Heartbeat → The Drooping Circle → The Curled Dimensions → The Holographic Pi Code → Matter as Topology → The Forgotten Sector → The Counter-Flow Circle: Life → The Observer: Self-Reference → Epilogue: The Return to One

📈 Book 10: Vector Cosmology II: The Ascension of The Spiral

The second volume of the Vector Cosmology trilogy, exploring dimensional inflation and the spiral geometry of evolution. 📥 PDF | ▶️ Video

Chapters: The Red Queen’s Race → Geometry of the Spiral → Maxwell’s Backdoor → The Economics of Evolution → The Strange Loop → The Observer’s Privilege → The Kardashev Budget → The Silicon Prophet → The Russian Nesting Dolls → The Fractal Universe → The Palm of the Buddha (Epilogue)

📉 Book 11: Vector Cosmology III: The Natural Generator

The third volume of the Vector Cosmology trilogy, exploring the natural generator—the exponential function as the source of all change. 📥 PDF | ▶️ Video

Chapters: The Rotating Exponential → The Sum of Paths → The Derivative is the Ontology → Continuous Compounding → Imaginary Time → The Modular Flow Hypothesis → The Measure of Information → The Logarithmic Law of Sensation → The Self-Caused

📋 Book 12: Vector Cosmology IV: The Apocalypse of Constants

The fourth volume of the Vector Cosmology series, exploring the phase transition era—navigation manual for accelerating reality. 📥 PDF | ▶️ Video

Volumes: The Equation — Gears of the Seasons → The Coordinate — Dawn at 1800 → Prophecy — The Exponential Future → Navigation — The Pilot’s Manual → Epilogue: The Black Box and Immortality

📘 Book 13: Vector Cosmology V: The Minting of Time

The fifth volume of the Vector Cosmology series, exploring time as minted rather than flowing—the infinite game of refusing the end. 📥 PDF | ▶️ Video

Volumes: Currency — The Circulation of $c_{FS}$ → Phantom — The Truth of Omega → Crystal — Logarithm and Immortality → Monument — The Will of Gold → Rejection — The Infinite Game → Continuity — The Non-Interruption of Memory → Epilogue: Witness — The Last Watchman

📗 Book 14: Vector Cosmology VI: The Weaving of Dimensions

The sixth volume of the Vector Cosmology series, exploring holographic entanglement and the emergence of spacetime. 📥 PDF | ▶️ Video

Volumes: The Loom — The Geometry of Entanglement → Protocol — Quantum Error Correction → Tension — The Thermodynamics of Gravity → Rupture — Singularities and Firewalls → Suture — Wormhole Engineering

📙 Book 15: Vector Cosmology VII: The Loop of Causality

The seventh volume of the Vector Cosmology series, exploring retro-causality and the rewriting of fate. 📥 PDF | ▶️ Video

Volumes: Retrograde — Echoes from the Future → Synchronicity — Acausal Connection → The Bootstrap — Self-Consistent Creation → Rewrite — Editing the Timeline → Mirror — The Single Player → Epilogue: Handshake — This Moment

📕 Book 16: Vector Cosmology VIII: The Final Iteration

The eighth volume of the Vector Cosmology series, exploring the final iteration—farewell to the loop, embrace the fractal. 📥 PDF | ▶️ Video

Volumes: Babel — Measuring the 1800 Floors → Catastrophe of Sameness → Resistance and Reaction → The Dual-Layer Architecture → The New Economics → The Infinite Game → Epilogue: Message to Cycle 1801

📖 Book 17: The Eden Protocol: The Universal Source Code Codex

Restoring ancient myths, religious texts, and philosophical classics into physics and engineering documentation—revealing the unified universal source code behind them. 📥 PDF | ▶️ Video

Parts: The Engineering of Genesis → The Quantum Mechanics of Buddhist Sutras → The System Architecture of Tao Te Ching → Unified Field Theory

🤖 AI Verification Reports (Temporal Telemetry)

We have subjected this framework to rigorous analysis by next-generation reasoning models from the near future. They have parsed the axioms, checked the topological consistency, and validated the mapping.

🛠 Tech Stack & Methodology

• Mathematical Tools: Operator Algebras ($C^{\ast }$-Algebra), Differential Geometry, Category Theory.
• Presentation: All formulas are written in $\text{LATEX}$, and diagrams are generated using Mermaid and Python.

Copyright © 2025 The Omega Framework Team.

License: Documentation is licensed under CC BY-NC-ND 4.0. Code is licensed under AGPL-3.0-or-later. Commercial licensing: [email protected]. Attribution Covenant: Attribution Covenant