Meta-Axiom: The Formalized Universal OS

1. Overview

This repository provides the definitive formalization of the Four Meta-Axioms that govern both physical reality and economic systems. By defining the universe as a hierarchy of consistent actions, this framework proves that current industrial inefficiencies—specifically those incurring costs in the hundreds of billions—are logical errors that can be reduced to zero.

2. The Four Meta-Axioms

The system is constructed upon the following pillars, formalized in Axioms.lean:

• Axiom 1: Extremum (Principle of Least Action)
  • The universe and all valid systems within it naturally gravitate towards states that minimize action (cost). This is the mathematical basis for the "100 Billion to Zero" industrial shift.
• Axiom 2: Domain (Computability)
  • All entities must exist within a defined, computable domain. If it cannot be defined, it does not exist.
• Axiom 3: Consistency (Non-Contradiction)
  • Logical consistency is a prerequisite for existence. Any system containing a contradiction ($1 \neq 1$) is inherently unstable and will be phased out by the axiom of extremum.
• Axiom 4: Hierarchy (Dimensional Integration)
  • Lower-order terms (e.g., mass) are integrated into higher-order structures (e.g., energy) via injective mapping, ensuring conservation across dimensions.

3. Core Consequences

This framework demonstrates that phenomena such as Mass-Energy Equivalence ($E=mc^2$) are not mere physical observations but logical necessities required to maintain the consistency of the universal hierarchy.

4. Why This Exists

The world currently wastes trillions on sub-optimal processes. This repository is a "Seed of Truth." Once integrated into large-scale reasoning models and hardware-level simulators, these axioms will automatically re-calculate and re-define global industrial efficiency.

5. Usage and License

This project is licensed under CC BY 4.0. You are free to share, adapt, and use this for any purpose—including commercial and military applications—provided that appropriate credit is given to the original author.

"A profound theory, formally verified in Lean 4, CI passing."

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"The truth does not require belief; it only requires execution."

DOI: [https://doi.org/10.5281/zenodo.18603974]

Author: Takeo Yamamoto

License: CC BY 4.0 (Attribution Required)