{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:WO2Q75TQE5EYQIU5NN44YDOSGK","short_pith_number":"pith:WO2Q75TQ","schema_version":"1.0","canonical_sha256":"b3b50ff670274988229d6b79cc0dd232959141aa66e75e490fabe7e5bf6accd2","source":{"kind":"arxiv","id":"2411.13374","version":2},"attestation_state":"computed","paper":{"title":"On the structure of normalized models of circular-arc graphs -- Hsu's approach revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Tomasz Krawczyk","submitted_at":"2024-11-20T14:52:43Z","abstract_excerpt":"Circular-arc graphs are the intersection graphs of arcs of a circle. The main result of this work describes the structure of all \\emph{normalized intersection models} of circular-arc graphs. Normalized models of a circular-arc graph reflect the neighborhood relation between its vertices and can be seen as its canonical representations; in particular, any intersection model can be made normalized by possibly extending some of its arcs. We~devise a data-structure, called \\emph{PQM-tree}, that maintains the set of all normalized models of a circular-arc graph. We show that the PQM-tree of a circu"},"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":"2411.13374","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-20T14:52:43Z","cross_cats_sorted":[],"title_canon_sha256":"a3321b09e90e734123ac3cce3ee7c5cb61783df22b88f519086332037641bece","abstract_canon_sha256":"647d896eb27ed4f3a6b23ca6e6713afb4a4b89a6af03b8403a39d59832001f0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:41:03.884333Z","signature_b64":"X4a+pq0G9uwWLd+xg2ALYrEB/oRMXf7gKIg+GN372a0sOam//dTw9iXqaA99QbJ810ZSerbcTYbO9pApcDPlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3b50ff670274988229d6b79cc0dd232959141aa66e75e490fabe7e5bf6accd2","last_reissued_at":"2026-07-05T09:41:03.883852Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:41:03.883852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the structure of normalized models of circular-arc graphs -- Hsu's approach revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Tomasz Krawczyk","submitted_at":"2024-11-20T14:52:43Z","abstract_excerpt":"Circular-arc graphs are the intersection graphs of arcs of a circle. The main result of this work describes the structure of all \\emph{normalized intersection models} of circular-arc graphs. Normalized models of a circular-arc graph reflect the neighborhood relation between its vertices and can be seen as its canonical representations; in particular, any intersection model can be made normalized by possibly extending some of its arcs. We~devise a data-structure, called \\emph{PQM-tree}, that maintains the set of all normalized models of a circular-arc graph. We show that the PQM-tree of a circu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13374","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13374/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.13374","created_at":"2026-07-05T09:41:03.883907+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.13374v2","created_at":"2026-07-05T09:41:03.883907+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13374","created_at":"2026-07-05T09:41:03.883907+00:00"},{"alias_kind":"pith_short_12","alias_value":"WO2Q75TQE5EY","created_at":"2026-07-05T09:41:03.883907+00:00"},{"alias_kind":"pith_short_16","alias_value":"WO2Q75TQE5EYQIU5","created_at":"2026-07-05T09:41:03.883907+00:00"},{"alias_kind":"pith_short_8","alias_value":"WO2Q75TQ","created_at":"2026-07-05T09:41:03.883907+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.13708","citing_title":"Comments on \"$\\mathcal{O}(m\\cdot n)$ algorithms for the recognition and isomorphism problems on circular-arc graphs\"","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK","json":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK.json","graph_json":"https://pith.science/api/pith-number/WO2Q75TQE5EYQIU5NN44YDOSGK/graph.json","events_json":"https://pith.science/api/pith-number/WO2Q75TQE5EYQIU5NN44YDOSGK/events.json","paper":"https://pith.science/paper/WO2Q75TQ"},"agent_actions":{"view_html":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK","download_json":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK.json","view_paper":"https://pith.science/paper/WO2Q75TQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.13374&json=true","fetch_graph":"https://pith.science/api/pith-number/WO2Q75TQE5EYQIU5NN44YDOSGK/graph.json","fetch_events":"https://pith.science/api/pith-number/WO2Q75TQE5EYQIU5NN44YDOSGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK/action/storage_attestation","attest_author":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK/action/author_attestation","sign_citation":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK/action/citation_signature","submit_replication":"https://pith.science/pith/WO2Q75TQE5EYQIU5NN44YDOSGK/action/replication_record"}},"created_at":"2026-07-05T09:41:03.883907+00:00","updated_at":"2026-07-05T09:41:03.883907+00:00"}