{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GG7542WXGCOWRWKYEY2YRULAXN","short_pith_number":"pith:GG7542WX","schema_version":"1.0","canonical_sha256":"31bfde6ad7309d68d958263588d160bb409aff395bdb5feff6da72f07a5d8a07","source":{"kind":"arxiv","id":"2603.21538","version":2},"attestation_state":"computed","paper":{"title":"Perfect divisibility and perfect-Pollyanna in bull-free graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Di Wu, Junran Yu, Paras Vinubhai Maniya, Ran Chen","submitted_at":"2026-03-23T03:46:17Z","abstract_excerpt":"A graph $G$ is {\\em perfectly divisible} if, for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\\omega(H[B])<\\omega(H)$. A {\\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Ho\\`ang [Discrete Math. 349 (2026) 114809] proposed four conjectures: 1. $P_5$-free graphs are perfectly divisible; 2. Odd hole-free graphs are perfectly divisible; 3. Even hole-free graphs are perfectly divisible; and 4. $4K_1$-free graphs are perfectly divisible. Karthick et al. [Electron. J. Combin. 29 (2022) P3.19] proposed a co"},"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":"2603.21538","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-23T03:46:17Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c1a753f18d4838a93cbf11d603e99fa38e23d9e40f64535aeec5af4162bf546c","abstract_canon_sha256":"b5f872678ba907ef44123b0c9c245efeb0d99a0e6648486e647f9db0a666dbe0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:16.285615Z","signature_b64":"Njw6M1DlNyagUWZa7iJxXXzIoob0EFSMiGVeFVOFLLWV3zRtE5oDHYnX5e8fVSCVrNgqI0HsQEO5owul02WeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31bfde6ad7309d68d958263588d160bb409aff395bdb5feff6da72f07a5d8a07","last_reissued_at":"2026-06-09T01:05:16.285170Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:16.285170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perfect divisibility and perfect-Pollyanna in bull-free graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Di Wu, Junran Yu, Paras Vinubhai Maniya, Ran Chen","submitted_at":"2026-03-23T03:46:17Z","abstract_excerpt":"A graph $G$ is {\\em perfectly divisible} if, for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\\omega(H[B])<\\omega(H)$. A {\\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Ho\\`ang [Discrete Math. 349 (2026) 114809] proposed four conjectures: 1. $P_5$-free graphs are perfectly divisible; 2. Odd hole-free graphs are perfectly divisible; 3. Even hole-free graphs are perfectly divisible; and 4. $4K_1$-free graphs are perfectly divisible. Karthick et al. [Electron. J. Combin. 29 (2022) P3.19] proposed a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21538","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/2603.21538/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":"2603.21538","created_at":"2026-06-09T01:05:16.285234+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.21538v2","created_at":"2026-06-09T01:05:16.285234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.21538","created_at":"2026-06-09T01:05:16.285234+00:00"},{"alias_kind":"pith_short_12","alias_value":"GG7542WXGCOW","created_at":"2026-06-09T01:05:16.285234+00:00"},{"alias_kind":"pith_short_16","alias_value":"GG7542WXGCOWRWKY","created_at":"2026-06-09T01:05:16.285234+00:00"},{"alias_kind":"pith_short_8","alias_value":"GG7542WX","created_at":"2026-06-09T01:05:16.285234+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/GG7542WXGCOWRWKYEY2YRULAXN","json":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN.json","graph_json":"https://pith.science/api/pith-number/GG7542WXGCOWRWKYEY2YRULAXN/graph.json","events_json":"https://pith.science/api/pith-number/GG7542WXGCOWRWKYEY2YRULAXN/events.json","paper":"https://pith.science/paper/GG7542WX"},"agent_actions":{"view_html":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN","download_json":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN.json","view_paper":"https://pith.science/paper/GG7542WX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.21538&json=true","fetch_graph":"https://pith.science/api/pith-number/GG7542WXGCOWRWKYEY2YRULAXN/graph.json","fetch_events":"https://pith.science/api/pith-number/GG7542WXGCOWRWKYEY2YRULAXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN/action/storage_attestation","attest_author":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN/action/author_attestation","sign_citation":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN/action/citation_signature","submit_replication":"https://pith.science/pith/GG7542WXGCOWRWKYEY2YRULAXN/action/replication_record"}},"created_at":"2026-06-09T01:05:16.285234+00:00","updated_at":"2026-06-09T01:05:16.285234+00:00"}