{"id":50533167,"url":"https://github.com/daedalus/alphaproof-nexus","last_synced_at":"2026-06-03T15:30:27.050Z","repository":{"id":359923780,"uuid":"1248028741","full_name":"daedalus/alphaproof-nexus","owner":"daedalus","description":"AlphaProof Nexus evolution on Erdős Problem #25 — does every congruence-avoiding set have a logarithmic density? Open problem, formalized in Lean 4.","archived":false,"fork":false,"pushed_at":"2026-05-24T07:03:32.000Z","size":75,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"master","last_synced_at":"2026-05-24T07:10:04.692Z","etag":null,"topics":["alphaproof-nexus","erdos-problems","formal-math","lean","lean4","open-problem","theorem-proving"],"latest_commit_sha":null,"homepage":null,"language":"Lean","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/daedalus.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,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":"AGENTS.md","dco":null,"cla":null}},"created_at":"2026-05-24T05:03:03.000Z","updated_at":"2026-05-24T07:03:36.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/daedalus/alphaproof-nexus","commit_stats":null,"previous_names":["daedalus/alphaproof-nexus"],"tags_count":null,"template":false,"template_full_name":null,"purl":"pkg:github/daedalus/alphaproof-nexus","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/daedalus%2Falphaproof-nexus","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/daedalus%2Falphaproof-nexus/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/daedalus%2Falphaproof-nexus/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/daedalus%2Falphaproof-nexus/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/daedalus","download_url":"https://codeload.github.com/daedalus/alphaproof-nexus/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/daedalus%2Falphaproof-nexus/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":33872297,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-06-03T02:00:06.370Z","response_time":59,"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":["alphaproof-nexus","erdos-problems","formal-math","lean","lean4","open-problem","theorem-proving"],"created_at":"2026-06-03T15:30:25.028Z","updated_at":"2026-06-03T15:30:27.043Z","avatar_url":"https://github.com/daedalus.png","language":"Lean","funding_links":[],"categories":[],"sub_categories":[],"readme":"# AlphaProof Nexus\n\nRepository of Lean 4 formalizations for open Erdős problems, evolved via\nAlphaProof Nexus (arXiv:2605.22763) evolutionary proof search.\n\n## Problems\n\n| # | Title | Status | Dir |\n|---|-------|--------|-----|\n| 1 | Sum-distinct sets | Proof complete (0 sorries) | `problems/1/` |\n| 25 | Congruence-avoiding sets | 10 sorries (1 open) | `problems/25/` |\n| 364 | Consecutive powerful numbers | 0 errors, 1 sorry | `problems/364/` |\n| 634 | Triangle tilings | 0 errors, 3 sorries | `problems/634/` |\n\nAll 628 open Erdős problems have directories under `problems/N/`.\n\n## Quick start\n\n```bash\nlean problems/25/Erdos25.lean\nlean problems/25/population/member_04_gen1_head_truncation.lean\nlean problems/634/population/member_07_gen7_geometric_obstruction.lean\nlean problems/1/Erdos1.lean\nlean problems/1/population/member_05_champion.lean\n```\n\nRequires Lean 4.29.1, `lean` on `PATH`.\n\nSee `AGENTS.md` for full workflow documentation.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdaedalus%2Falphaproof-nexus","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdaedalus%2Falphaproof-nexus","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdaedalus%2Falphaproof-nexus/lists"}