{"id":17717324,"url":"https://github.com/bwesterb/ks","last_synced_at":"2025-08-09T01:41:09.630Z","repository":{"id":17481259,"uuid":"20261673","full_name":"bwesterb/ks","owner":"bwesterb","description":null,"archived":false,"fork":false,"pushed_at":"2023-07-04T09:00:08.000Z","size":7273,"stargazers_count":4,"open_issues_count":0,"forks_count":1,"subscribers_count":2,"default_branch":"master","last_synced_at":"2023-07-04T10:06:56.681Z","etag":null,"topics":["kochen-specker","latex","math"],"latest_commit_sha":null,"homepage":"kochen-specker.info","language":"Makefile","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/bwesterb.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"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}},"created_at":"2014-05-28T15:00:55.000Z","updated_at":"2023-07-03T14:55:13.000Z","dependencies_parsed_at":"2024-10-25T22:55:26.044Z","dependency_job_id":null,"html_url":"https://github.com/bwesterb/ks","commit_stats":null,"previous_names":[],"tags_count":9,"template":null,"template_full_name":null,"purl":"pkg:github/bwesterb/ks","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bwesterb%2Fks","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bwesterb%2Fks/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bwesterb%2Fks/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bwesterb%2Fks/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/bwesterb","download_url":"https://codeload.github.com/bwesterb/ks/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bwesterb%2Fks/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":269518552,"owners_count":24430631,"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":"2025-08-08T02:00:09.200Z","response_time":72,"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":["kochen-specker","latex","math"],"created_at":"2024-10-25T14:19:50.484Z","updated_at":"2025-08-09T01:41:09.577Z","avatar_url":"https://github.com/bwesterb.png","language":"Makefile","funding_links":[],"categories":[],"sub_categories":[],"readme":"A Kochen-Specker System has at least 22 vertices\n================================================\n\n* Bas Westerbaan (bas@westerbaan.name)\n* Sander Uijlen (suijlen1337@gmail.com)\n\nAbstract\n--------\nAt the heart of the Conway-Kochen Free Will theorem and Kochen and\nSpecker's argument against non-contextual hidden variable theories\nis the existence of a Kochen-Specker (KS) system: a set of points\non the sphere that has no {0, 1}-coloring such that at most one of\ntwo orthogonal points are colored 1 and of three pairwise orthogonal\npoints exactly one is colored 1. In public lectures, Conway\nencouraged the search for small KS systems. At the time of writing,\nthe smallest known KS system has 31 vectors.  Arends, Ouaknine and\nWampler have shown that a KS system has at least 18 vectors, by\nreducing the problem to the existence of graphs with a topological\nembeddability and non-colorability property. The bottleneck in their\nsearch proved to be the sheer number of graphs on more than 17\nvertices and deciding embeddability.  Continuing their effort, we\nprove a restriction on the class of graphs we need to consider and\ndevelop a more practical decision procedure for embeddability to\nimprove the lower bound to 22. In 2022, Li, Bright, and Ganesh improved\nthe lower bound to 23, then shortly after to 24 in 2023 using a SAT solver + \nComputer Algebra System approach to dramatically reduce the search space.\n\nThis repository\n---------------\n\nThis repository contains the\n\n * LaTeX sourcecode of the preprint (under `/paper`);\n * LaTeX sourcecode for the slides used at QPL2014 (under `/qpl2014`);\n * Data generated by some of the computations (under `/graphs`);\n * source code used for the computation (under `/code`,\n   in particular `/code/comp\u003cn\u003e.py`) and\n * source code of the website kochen-specker.info (under `/site`).\n    * First, in `/code`, run `python generateSite.py`.\n    * Then, in  `/site`, run `jekyll build`.\n    * Find the site in `/site/_site`.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbwesterb%2Fks","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fbwesterb%2Fks","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbwesterb%2Fks/lists"}