{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:D5QG2YBM5M3BK6T6AIWAG4BVC6","short_pith_number":"pith:D5QG2YBM","schema_version":"1.0","canonical_sha256":"1f606d602ceb36157a7e022c03703517a5f066139a69247c9013b9622fc5667e","source":{"kind":"arxiv","id":"1609.07768","version":3},"attestation_state":"computed","paper":{"title":"On semitopological interassociates of the bicyclic monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Kateryna Maksymyk, Oleg Gutik","submitted_at":"2016-09-25T16:31:03Z","abstract_excerpt":"Semitopological interassociates $\\mathscr{C}_{m,n}$ of the bicyclic semigroup $\\mathscr{C}(p,q)$ are studied. In particular, we show that for arbitrary non-negative integers $m$, $n$ and every Hausdorff topology $\\tau$ on $\\mathscr{C}_{m,n}$ such that $\\left(\\mathscr{C}_{m,n},\\tau\\right)$ is a semitopological semigroup, is discrete. Also, we prove that if an interassociate of the bicyclic monoid $\\mathscr{C}_{m,n}$ is a dense subsemigroup of a Hausdorff semitopological semigroup $(S,\\cdot)$ and $I=S\\setminus\\mathscr{C}_{m,n}\\neq\\varnothing$ then $I$ is a two-sided ideal of the semigroup $S$ an"},"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":"1609.07768","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-25T16:31:03Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"033693b72236db29f632c0cd3d0f6cb40ac293fcc4572e7ba6f4a57a76bc2476","abstract_canon_sha256":"95a43dd71d104753b592f12997e7f9410e5974252c368a5e7a3fc7e84a7e96ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:01.493366Z","signature_b64":"aqDD0/ZxK5W9OSg4lzGGFu4N2G9m3ae1KKtx3HskvUBVAb7P7BkK1B3r6I5KB7piUzbXvYKNUATG2Ui6T9Q1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f606d602ceb36157a7e022c03703517a5f066139a69247c9013b9622fc5667e","last_reissued_at":"2026-05-18T00:45:01.493003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:01.493003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On semitopological interassociates of the bicyclic monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Kateryna Maksymyk, Oleg Gutik","submitted_at":"2016-09-25T16:31:03Z","abstract_excerpt":"Semitopological interassociates $\\mathscr{C}_{m,n}$ of the bicyclic semigroup $\\mathscr{C}(p,q)$ are studied. In particular, we show that for arbitrary non-negative integers $m$, $n$ and every Hausdorff topology $\\tau$ on $\\mathscr{C}_{m,n}$ such that $\\left(\\mathscr{C}_{m,n},\\tau\\right)$ is a semitopological semigroup, is discrete. Also, we prove that if an interassociate of the bicyclic monoid $\\mathscr{C}_{m,n}$ is a dense subsemigroup of a Hausdorff semitopological semigroup $(S,\\cdot)$ and $I=S\\setminus\\mathscr{C}_{m,n}\\neq\\varnothing$ then $I$ is a two-sided ideal of the semigroup $S$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07768","kind":"arxiv","version":3},"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":"1609.07768","created_at":"2026-05-18T00:45:01.493059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07768v3","created_at":"2026-05-18T00:45:01.493059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07768","created_at":"2026-05-18T00:45:01.493059+00:00"},{"alias_kind":"pith_short_12","alias_value":"D5QG2YBM5M3B","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"D5QG2YBM5M3BK6T6","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"D5QG2YBM","created_at":"2026-05-18T12:30:09.641336+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/D5QG2YBM5M3BK6T6AIWAG4BVC6","json":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6.json","graph_json":"https://pith.science/api/pith-number/D5QG2YBM5M3BK6T6AIWAG4BVC6/graph.json","events_json":"https://pith.science/api/pith-number/D5QG2YBM5M3BK6T6AIWAG4BVC6/events.json","paper":"https://pith.science/paper/D5QG2YBM"},"agent_actions":{"view_html":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6","download_json":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6.json","view_paper":"https://pith.science/paper/D5QG2YBM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07768&json=true","fetch_graph":"https://pith.science/api/pith-number/D5QG2YBM5M3BK6T6AIWAG4BVC6/graph.json","fetch_events":"https://pith.science/api/pith-number/D5QG2YBM5M3BK6T6AIWAG4BVC6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6/action/storage_attestation","attest_author":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6/action/author_attestation","sign_citation":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6/action/citation_signature","submit_replication":"https://pith.science/pith/D5QG2YBM5M3BK6T6AIWAG4BVC6/action/replication_record"}},"created_at":"2026-05-18T00:45:01.493059+00:00","updated_at":"2026-05-18T00:45:01.493059+00:00"}