{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:234HABOSOBLZUMBKW7MR7JPQCC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf27fd5f20cc07621437fcec6c5f2989c1c3e22b77d7724b41f044b0d2d66104","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-20T20:58:08Z","title_canon_sha256":"65b300b0e934bf728eb0bad7fb6833cbc5e0055b068674047b084cce5bbeb56d"},"schema_version":"1.0","source":{"id":"2411.13708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13708","created_at":"2026-07-05T09:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13708v2","created_at":"2026-07-05T09:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13708","created_at":"2026-07-05T09:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"234HABOSOBLZ","created_at":"2026-07-05T09:40:44Z"},{"alias_kind":"pith_short_16","alias_value":"234HABOSOBLZUMBK","created_at":"2026-07-05T09:40:44Z"},{"alias_kind":"pith_short_8","alias_value":"234HABOS","created_at":"2026-07-05T09:40:44Z"}],"graph_snapshots":[{"event_id":"sha256:5ba5404c3f319ea96164b64d64a56512692d3abfd931670ffec6de84a9b9e13f","target":"graph","created_at":"2026-07-05T09:40:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.13708/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the work [$\\mathcal{O}(m\\cdot n)$ algorithms for the recognition and isomorphism problems on circular-arc graphs, SIAM J. Comput. 24(3), 411--439, (1995)], Wen-Lian Hsu claims three results concerning the class of circular-arc graphs: - the design of so-called \\emph{decomposition trees} that represent the structure of all normalized intersection models of circular-arc graphs, - an $\\mathcal{O}(m\\cdot n)$ recognition algorithm for circular-arc graphs, - an $\\mathcal{O}(m\\cdot n)$ isomorphism algorithm for circular-arc graphs. In [Discrete Math. Theor. Comput. Sci., 15(1), 157--182, 2013] Cur","authors_text":"Tomasz Krawczyk","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-20T20:58:08Z","title":"Comments on \"$\\mathcal{O}(m\\cdot n)$ algorithms for the recognition and isomorphism problems on circular-arc graphs\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13708","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8e051c1d671a535076b4723c3372d4f6552b989d3afc8d0a79e375e94232bcae","target":"record","created_at":"2026-07-05T09:40:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf27fd5f20cc07621437fcec6c5f2989c1c3e22b77d7724b41f044b0d2d66104","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-20T20:58:08Z","title_canon_sha256":"65b300b0e934bf728eb0bad7fb6833cbc5e0055b068674047b084cce5bbeb56d"},"schema_version":"1.0","source":{"id":"2411.13708","kind":"arxiv","version":2}},"canonical_sha256":"d6f87005d270579a302ab7d91fa5f010ac324f46b1e126f7805c961bfef6f843","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6f87005d270579a302ab7d91fa5f010ac324f46b1e126f7805c961bfef6f843","first_computed_at":"2026-07-05T09:40:44.761797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:44.761797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cWtMYJJDe4oglwA8SjFbsqeA6lNjxqWFz6HytroRmTEPsbPfIdzBQ50FJzcszkA5FGAFpnaWezaROwlho0haBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:44.762229Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e051c1d671a535076b4723c3372d4f6552b989d3afc8d0a79e375e94232bcae","sha256:5ba5404c3f319ea96164b64d64a56512692d3abfd931670ffec6de84a9b9e13f"],"state_sha256":"8db4cfa141b913cc0ad0f0cbb8419526d0645e79f57d98412af8989633ec3d15"}