{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:L55Z5PJDVESDNXZO23CJIJZ5Y5","short_pith_number":"pith:L55Z5PJD","schema_version":"1.0","canonical_sha256":"5f7b9ebd23a92436df2ed6c494273dc74293e2340d17e7b80aaf004e29481e04","source":{"kind":"arxiv","id":"1205.4960","version":2},"attestation_state":"computed","paper":{"title":"Orbit coherence in permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"John R. Britnell, Mark Wildon","submitted_at":"2012-05-22T16:13:34Z","abstract_excerpt":"This paper introduces the notion of orbit coherence in a permutation group. Let $G$ be a group of permutations of a set $\\Omega$. Let $\\pi(G)$ be the set of partitions of $\\Omega$ which arise as the orbit partition of an element of $G$. The set of partitions of $\\Omega$ is naturally ordered by refinement, and admits join and meet operations. We say that $G$ is join-coherent if $\\pi(G)$ is join-closed, and meet-coherent if $\\pi(G)$ is meet-closed.\n  Our central theorem states that the centralizer in $\\Sym(\\Omega)$ of any permutation $g$ is meet-coherent, and subject to a certain finiteness cond"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.4960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-05-22T16:13:34Z","cross_cats_sorted":[],"title_canon_sha256":"53c6a8955891b3a324ccd00edf36fef4e42ff7dde2aba18ce9510e74cc2b6db4","abstract_canon_sha256":"8eb1961b9793bfd636958c616892345ad4067cab1be2f3193e75143434216b5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:25.406755Z","signature_b64":"5CoBUkz9d8qPl+RBJ6VUSTrSJRhklsfO+NAZ7dhOYLU+pX1sjOHjTfrYtTnTJh34YKp7G6c1NyyhW17fJVi0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f7b9ebd23a92436df2ed6c494273dc74293e2340d17e7b80aaf004e29481e04","last_reissued_at":"2026-05-18T03:54:25.406250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:25.406250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orbit coherence in permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"John R. Britnell, Mark Wildon","submitted_at":"2012-05-22T16:13:34Z","abstract_excerpt":"This paper introduces the notion of orbit coherence in a permutation group. Let $G$ be a group of permutations of a set $\\Omega$. Let $\\pi(G)$ be the set of partitions of $\\Omega$ which arise as the orbit partition of an element of $G$. The set of partitions of $\\Omega$ is naturally ordered by refinement, and admits join and meet operations. We say that $G$ is join-coherent if $\\pi(G)$ is join-closed, and meet-coherent if $\\pi(G)$ is meet-closed.\n  Our central theorem states that the centralizer in $\\Sym(\\Omega)$ of any permutation $g$ is meet-coherent, and subject to a certain finiteness cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4960","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.4960","created_at":"2026-05-18T03:54:25.406326+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.4960v2","created_at":"2026-05-18T03:54:25.406326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4960","created_at":"2026-05-18T03:54:25.406326+00:00"},{"alias_kind":"pith_short_12","alias_value":"L55Z5PJDVESD","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"L55Z5PJDVESDNXZO","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"L55Z5PJD","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5","json":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5.json","graph_json":"https://pith.science/api/pith-number/L55Z5PJDVESDNXZO23CJIJZ5Y5/graph.json","events_json":"https://pith.science/api/pith-number/L55Z5PJDVESDNXZO23CJIJZ5Y5/events.json","paper":"https://pith.science/paper/L55Z5PJD"},"agent_actions":{"view_html":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5","download_json":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5.json","view_paper":"https://pith.science/paper/L55Z5PJD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.4960&json=true","fetch_graph":"https://pith.science/api/pith-number/L55Z5PJDVESDNXZO23CJIJZ5Y5/graph.json","fetch_events":"https://pith.science/api/pith-number/L55Z5PJDVESDNXZO23CJIJZ5Y5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5/action/storage_attestation","attest_author":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5/action/author_attestation","sign_citation":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5/action/citation_signature","submit_replication":"https://pith.science/pith/L55Z5PJDVESDNXZO23CJIJZ5Y5/action/replication_record"}},"created_at":"2026-05-18T03:54:25.406326+00:00","updated_at":"2026-05-18T03:54:25.406326+00:00"}