{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FS74DGC4APHRKDBSARHRYDXC3L","short_pith_number":"pith:FS74DGC4","schema_version":"1.0","canonical_sha256":"2cbfc1985c03cf150c32044f1c0ee2daeee90f91f7d988fd62c75776baedc7aa","source":{"kind":"arxiv","id":"1209.4796","version":1},"attestation_state":"computed","paper":{"title":"Stationary Sets in Topological and Paratopological Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Cetin Vural, Raushan Buzyakova","submitted_at":"2012-09-21T12:09:48Z","abstract_excerpt":"We show that if a topological or paratopological group $G$ contains a stationary subset of some regular uncountable cardinal, then $G$ contains a subspace which is not collectionwise normal. This statement implies that if a monotonically normal space (in particular, any generalized ordered space) is a paratopological group then the space is hereditarily paracompact."},"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":"1209.4796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-09-21T12:09:48Z","cross_cats_sorted":[],"title_canon_sha256":"1224954041581a6a3038e1ff25fd529da97c9f4dfc86d2998cf2b1e1b08efb67","abstract_canon_sha256":"ebca35a29f795bf9e2e15436c22ba6a05d17f2796d3440de0b53ede624a03f18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:09.907555Z","signature_b64":"CIy9aGUV56NRamQVMdDwJ0vt5jYO4WAfDOSq+1edhYfHhxg2aqeVcgjmFWC2QMlM5+k3kSysfElY9HR+YRzeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cbfc1985c03cf150c32044f1c0ee2daeee90f91f7d988fd62c75776baedc7aa","last_reissued_at":"2026-05-18T03:45:09.907028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:09.907028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary Sets in Topological and Paratopological Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Cetin Vural, Raushan Buzyakova","submitted_at":"2012-09-21T12:09:48Z","abstract_excerpt":"We show that if a topological or paratopological group $G$ contains a stationary subset of some regular uncountable cardinal, then $G$ contains a subspace which is not collectionwise normal. This statement implies that if a monotonically normal space (in particular, any generalized ordered space) is a paratopological group then the space is hereditarily paracompact."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4796","kind":"arxiv","version":1},"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":"1209.4796","created_at":"2026-05-18T03:45:09.907120+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4796v1","created_at":"2026-05-18T03:45:09.907120+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4796","created_at":"2026-05-18T03:45:09.907120+00:00"},{"alias_kind":"pith_short_12","alias_value":"FS74DGC4APHR","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FS74DGC4APHRKDBS","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FS74DGC4","created_at":"2026-05-18T12:27:06.952714+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/FS74DGC4APHRKDBSARHRYDXC3L","json":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L.json","graph_json":"https://pith.science/api/pith-number/FS74DGC4APHRKDBSARHRYDXC3L/graph.json","events_json":"https://pith.science/api/pith-number/FS74DGC4APHRKDBSARHRYDXC3L/events.json","paper":"https://pith.science/paper/FS74DGC4"},"agent_actions":{"view_html":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L","download_json":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L.json","view_paper":"https://pith.science/paper/FS74DGC4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4796&json=true","fetch_graph":"https://pith.science/api/pith-number/FS74DGC4APHRKDBSARHRYDXC3L/graph.json","fetch_events":"https://pith.science/api/pith-number/FS74DGC4APHRKDBSARHRYDXC3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L/action/storage_attestation","attest_author":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L/action/author_attestation","sign_citation":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L/action/citation_signature","submit_replication":"https://pith.science/pith/FS74DGC4APHRKDBSARHRYDXC3L/action/replication_record"}},"created_at":"2026-05-18T03:45:09.907120+00:00","updated_at":"2026-05-18T03:45:09.907120+00:00"}