{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ROALM3RNTEVI5EKDQ656IICUSV","short_pith_number":"pith:ROALM3RN","schema_version":"1.0","canonical_sha256":"8b80b66e2d992a8e914387bbe420549564f498994e0881a723589e5096117949","source":{"kind":"arxiv","id":"1807.03768","version":1},"attestation_state":"computed","paper":{"title":"Induced subgraphs of graphs with large chromatic number. XIII. New brooms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Paul Seymour","submitted_at":"2018-07-10T17:44:46Z","abstract_excerpt":"Gy\\'arf\\'as and Sumner independently conjectured that for every tree $T$, the class of graphs not containing $T$ as an induced subgraph is $\\chi$-bounded, that is, the chromatic numbers of graphs in this class are bounded above by a function of their clique numbers. This remains open for general trees $T$, but has been proved for some particular trees. For $k\\ge 1$, let us say a broom of length $k$ is a tree obtained from a $k$-edge path with ends $a,b$ by adding some number of leaves adjacent to $b$, and we call $a$ its handle. A tree obtained from brooms of lengths $k_1,...,k_n$ by identifyi"},"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":"1807.03768","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-10T17:44:46Z","cross_cats_sorted":[],"title_canon_sha256":"73b0c93377bd034928db8655c4eec02a321c806af30df04b98d07941e3d85042","abstract_canon_sha256":"f91c06750aeeadf5bebc1e922b24b8b602e5819c5fc56d699ea9b2484e563196"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:00.991794Z","signature_b64":"KGe/aJNFmOBiihmsCcTITSfhc9ZF1NosfW86BZEnrF3ucl+BFNG5vWtCFiFY6IMMPeSWWo4NoAcsj5Gi8hNgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b80b66e2d992a8e914387bbe420549564f498994e0881a723589e5096117949","last_reissued_at":"2026-05-18T00:11:00.991079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:00.991079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Induced subgraphs of graphs with large chromatic number. XIII. New brooms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Paul Seymour","submitted_at":"2018-07-10T17:44:46Z","abstract_excerpt":"Gy\\'arf\\'as and Sumner independently conjectured that for every tree $T$, the class of graphs not containing $T$ as an induced subgraph is $\\chi$-bounded, that is, the chromatic numbers of graphs in this class are bounded above by a function of their clique numbers. This remains open for general trees $T$, but has been proved for some particular trees. For $k\\ge 1$, let us say a broom of length $k$ is a tree obtained from a $k$-edge path with ends $a,b$ by adding some number of leaves adjacent to $b$, and we call $a$ its handle. A tree obtained from brooms of lengths $k_1,...,k_n$ by identifyi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03768","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":"1807.03768","created_at":"2026-05-18T00:11:00.991207+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03768v1","created_at":"2026-05-18T00:11:00.991207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03768","created_at":"2026-05-18T00:11:00.991207+00:00"},{"alias_kind":"pith_short_12","alias_value":"ROALM3RNTEVI","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"ROALM3RNTEVI5EKD","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"ROALM3RN","created_at":"2026-05-18T12:32:50.500415+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/ROALM3RNTEVI5EKDQ656IICUSV","json":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV.json","graph_json":"https://pith.science/api/pith-number/ROALM3RNTEVI5EKDQ656IICUSV/graph.json","events_json":"https://pith.science/api/pith-number/ROALM3RNTEVI5EKDQ656IICUSV/events.json","paper":"https://pith.science/paper/ROALM3RN"},"agent_actions":{"view_html":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV","download_json":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV.json","view_paper":"https://pith.science/paper/ROALM3RN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03768&json=true","fetch_graph":"https://pith.science/api/pith-number/ROALM3RNTEVI5EKDQ656IICUSV/graph.json","fetch_events":"https://pith.science/api/pith-number/ROALM3RNTEVI5EKDQ656IICUSV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV/action/storage_attestation","attest_author":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV/action/author_attestation","sign_citation":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV/action/citation_signature","submit_replication":"https://pith.science/pith/ROALM3RNTEVI5EKDQ656IICUSV/action/replication_record"}},"created_at":"2026-05-18T00:11:00.991207+00:00","updated_at":"2026-05-18T00:11:00.991207+00:00"}