{"id":30860383,"url":"https://github.com/selfapplied/keya","last_synced_at":"2025-10-05T15:32:48.776Z","repository":{"id":302793263,"uuid":"1011274657","full_name":"selfapplied/keya","owner":"selfapplied","description":null,"archived":false,"fork":false,"pushed_at":"2025-07-04T08:19:40.000Z","size":542,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2025-07-04T09:30:55.932Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"other","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/selfapplied.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null}},"created_at":"2025-06-30T15:05:37.000Z","updated_at":"2025-07-04T08:19:44.000Z","dependencies_parsed_at":"2025-07-04T09:32:23.307Z","dependency_job_id":"b00fbb7d-642b-4ab0-a6ae-11ef2eaf00d8","html_url":"https://github.com/selfapplied/keya","commit_stats":null,"previous_names":["selfapplied/keya"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/selfapplied/keya","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/selfapplied%2Fkeya","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/selfapplied%2Fkeya/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/selfapplied%2Fkeya/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/selfapplied%2Fkeya/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/selfapplied","download_url":"https://codeload.github.com/selfapplied/keya/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/selfapplied%2Fkeya/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":274058943,"owners_count":25215200,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","status":"online","status_checked_at":"2025-09-07T02:00:09.463Z","response_time":67,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2025-09-07T15:44:23.438Z","updated_at":"2025-10-05T15:32:43.744Z","avatar_url":"https://github.com/selfapplied.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Kéya: An Engine for Symbolic Calculus\n\nKéya 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.\n\nThe 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.\n\n## The Σ-Calculus\n\nThe core theory behind Kéya is the \"Σ-Calculus,\" a paradigm built on a few key principles:\n\n*   **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.\n*   **Universal Transformations**: A minimal set of universal operators are applied to these fields. These operators are not complex functions but fundamental, combinatorial transformations.\n*   **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.\n*   **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.\n\n## The `PascalKernel`: A Concrete Implementation\n\nThe primary engine implementing the Σ-Calculus today is the `PascalKernel`.\n\nThis 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.\n\n## Exploring the Proofs\n\nThe 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.\n\nTo see a comprehensive overview, generate the interactive HTML report:\n\n```bash\npython -m keya.reporting.builder\n```\n\nThis 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:\n\n*   **Formal Arithmetic**: Simulating the subtle, emergent behaviors of floating-point arithmetic using the engine's fundamental binary logic.\n*   **Physical Phenomena**: Generating the shapes of quantum atomic orbitals and modeling the evolution of wavefunctions.\n*   **Complex Systems**: Running cellular automata and other generative models to show how complex patterns can emerge from simple, local rules.\n*   **Declarative Pipelines**: Executing high-level, declarative experimental pipelines via the K-Shell DSL.\n\n## License\n\nKéya 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.","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fselfapplied%2Fkeya","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fselfapplied%2Fkeya","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fselfapplied%2Fkeya/lists"}