https://github.com/selfapplied/keya
https://github.com/selfapplied/keya
Last synced: 8 months ago
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- Host: GitHub
- URL: https://github.com/selfapplied/keya
- Owner: selfapplied
- License: other
- Created: 2025-06-30T15:05:37.000Z (12 months ago)
- Default Branch: main
- Last Pushed: 2025-07-04T08:19:40.000Z (11 months ago)
- Last Synced: 2025-07-04T09:30:55.932Z (11 months ago)
- Language: Python
- Size: 529 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Kéya: An Engine for Symbolic Calculus
Kéya is an experimental computational framework for exploring a core hypothesis: that a vast range of computational systems can be modeled as emergent behaviors of a single, universal, symbolic calculus.
The philosophy of Kéya is not to build a specific tool for a specific problem, but to develop a fundamental "computational substrate" and then discover novel **representations** of problems that can be solved by the substrate's intrinsic rules.
## The Σ-Calculus
The core theory behind Kéya is the "Σ-Calculus," a paradigm built on a few key principles:
* **Symbolic Fields**: The state of any system is represented not as a single value, but as a field or vector of symbolic units. A number can be a vector of its digits; a physical system can be a field of quantum states.
* **Universal Transformations**: A minimal set of universal operators are applied to these fields. These operators are not complex functions but fundamental, combinatorial transformations.
* **Computation as Normalization**: The result of a transformation is often an unstable, "un-normalized" state. The crucial step of computation is applying a universal "carry" or "reduction" rule that propagates through the state until it re-stabilizes.
* **Emergent Complexity**: Complex, high-level behaviors—the rules of arithmetic, the shapes of orbitals, the patterns of a cellular automaton—are hypothesized to be emergent properties of the simple, underlying normalization rules.
## The `PascalKernel`: A Concrete Implementation
The primary engine implementing the Σ-Calculus today is the `PascalKernel`.
This is a pure, parameter-free mathematical object whose normalization rules are derived from the combinatorial properties of Pascal's triangle modulo 2 (the Sierpinski triangle). It provides a concrete, powerful, and surprisingly versatile foundation for testing the calculus's claims.
## Exploring the Proofs
The best way to understand Kéya is to explore the demos. They are not just examples; they are rigorous, assertion-backed proofs that test the core hypothesis against real-world computational systems.
To see a comprehensive overview, generate the interactive HTML report:
```bash
python -m keya.reporting.builder
```
This command runs all registered demos and creates a detailed report in `.out/report.html`, complete with visualizations, claims, and findings for each experiment. The demos prove that the engine can successfully model:
* **Formal Arithmetic**: Simulating the subtle, emergent behaviors of floating-point arithmetic using the engine's fundamental binary logic.
* **Physical Phenomena**: Generating the shapes of quantum atomic orbitals and modeling the evolution of wavefunctions.
* **Complex Systems**: Running cellular automata and other generative models to show how complex patterns can emerge from simple, local rules.
* **Declarative Pipelines**: Executing high-level, declarative experimental pipelines via the K-Shell DSL.
## License
Kéya is released under the [GNU Affero General Public License v3.0](LICENSE) (AGPL-3.0), chosen to foster community, sharing, and reinvestment in the project's development.