{"id":43086048,"url":"https://github.com/inaciovasquez2020/cycle-local-rigidity","last_synced_at":"2026-04-26T16:02:24.875Z","repository":{"id":334156656,"uuid":"1140210227","full_name":"inaciovasquez2020/cycle-local-rigidity","owner":"inaciovasquez2020","description":"Cycle-Local Rigidity — locality-based rigidity from cycle structure; executable witnesses and proofs of local-to-global obstruction.","archived":false,"fork":false,"pushed_at":"2026-04-13T10:41:53.000Z","size":866,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-04-13T12:29:27.887Z","etag":null,"topics":["cycle-local-rigidity","cycles","formal-methods","formal-verification","graph-theory","invariants","lean4","locality","mathlib","reproducible-research","rigidity-theory","unified-rigidity-framework"],"latest_commit_sha":null,"homepage":" https://inaciovasquez2020.github.io","language":"TeX","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/inaciovasquez2020.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2026-01-23T01:06:34.000Z","updated_at":"2026-04-13T10:41:58.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/inaciovasquez2020/cycle-local-rigidity","commit_stats":null,"previous_names":["inaciovasquez2020/cycle-local-rigidity"],"tags_count":9,"template":false,"template_full_name":null,"purl":"pkg:github/inaciovasquez2020/cycle-local-rigidity","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/inaciovasquez2020%2Fcycle-local-rigidity","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/inaciovasquez2020%2Fcycle-local-rigidity/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/inaciovasquez2020%2Fcycle-local-rigidity/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/inaciovasquez2020%2Fcycle-local-rigidity/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/inaciovasquez2020","download_url":"https://codeload.github.com/inaciovasquez2020/cycle-local-rigidity/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/inaciovasquez2020%2Fcycle-local-rigidity/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":32303177,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-04-26T09:34:17.070Z","status":"ssl_error","status_checked_at":"2026-04-26T09:34:00.993Z","response_time":129,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"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":["cycle-local-rigidity","cycles","formal-methods","formal-verification","graph-theory","invariants","lean4","locality","mathlib","reproducible-research","rigidity-theory","unified-rigidity-framework"],"created_at":"2026-01-31T15:10:15.726Z","updated_at":"2026-04-26T16:02:24.871Z","avatar_url":"https://github.com/inaciovasquez2020.png","language":"TeX","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Cycle Local Rigidity\n\n![CI](https://github.com/inaciovasquez2020/cycle-local-rigidity/actions/workflows/ci.yml/badge.svg)\n\n# Cycle–Local Rigidity (bounded verification)\n\nBounded, exhaustive verification of a cycle–local rigidity implication for finite graphs.\n\n## Result (bounded)\nFix parameters ρ₀ = 1 and C₀ = 1. For all graphs G with at most 7 vertices satisfying:\n- maximum degree Δ(G) ≤ 4\n- Ihara–Bass / nonbacktracking spectral condition IB_{ρ₀}\n- FO^4 radius-2 homogeneity\n\nno counterexample exists to:\nIB_{ρ₀} ⇒ CLR(4,4,2; ρ₀, C₀)\n\n## Method\nAll graphs up to n ≤ 7 are exhaustively enumerated and filtered by:\n- nonbacktracking / Ihara–Bass spectral verifier\n- FO^4 radius-2 homogeneity checker\n- local F₂ cycle-rank checker\n\nVerification is deterministic and enforced by CI.\n\n## Status / Scope\n- Verified: n ≤ 7 (bounded exhaustive)\n- Not claimed: any unbounded-n theorem\n- n ≥ 8: infeasible without additional structure\n\n## Quickstart\n```bash\n./verify.sh\nArtifacts\ncertificate.json\ncertificate.sha256\nCitation\nSee CITATION.cff.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Finaciovasquez2020%2Fcycle-local-rigidity","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Finaciovasquez2020%2Fcycle-local-rigidity","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Finaciovasquez2020%2Fcycle-local-rigidity/lists"}