{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GUKVCL5CYSKQDDQSUS6HIE36T5","short_pith_number":"pith:GUKVCL5C","schema_version":"1.0","canonical_sha256":"3515512fa2c495018e12a4bc74137e9f67ea992dc269042a2b4fd19a2e7d7a2b","source":{"kind":"arxiv","id":"1611.06142","version":2},"attestation_state":"computed","paper":{"title":"Balanced independent sets in graphs omitting large cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Andres A. Lopez, Claude Laflamme, Daniel T. Soukup, Robert Woodrow","submitted_at":"2016-11-18T16:17:19Z","abstract_excerpt":"Our goal is to investigate a close relative of the independent transversal problem in the class of infinite $K_n$-free graphs: we show that for any infinite $K_n$-free graph $G=(V,E)$ and $m\\in \\mathbb N$ there is a minimal $r=r(G,m)$ such that for any balanced $r$-colouring of the vertices of $G$ one can find an independent set which meets at least $m$ colour classes in a set of size $|V|$. Answering a conjecture of S. Thomass\\'e, we express the exact value of $r(H_n,m)$ (using Ramsey-numbers for finite digraphs), where $H_n$ is Henson's countable universal homogeneous $K_n$-free graph. In tu"},"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":"1611.06142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T16:17:19Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"1737dc8871ba39f34d4ba57b47a4adbd37b9305bb2191a2a41c28fd78848b389","abstract_canon_sha256":"9305b738a9a60ca09870ef9e4ec3aa546ae8cfa5377defb2e7a0304e91775ee3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:18.208973Z","signature_b64":"PusSdUPGZLrjn+db8MSNrfIqIlDct232NG3mfDnmVBEEGWm96WG3YZnxvQJu6oBJrntnMy+rZ1GC9m+rHRs+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3515512fa2c495018e12a4bc74137e9f67ea992dc269042a2b4fd19a2e7d7a2b","last_reissued_at":"2026-05-18T00:43:18.208248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:18.208248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Balanced independent sets in graphs omitting large cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Andres A. Lopez, Claude Laflamme, Daniel T. Soukup, Robert Woodrow","submitted_at":"2016-11-18T16:17:19Z","abstract_excerpt":"Our goal is to investigate a close relative of the independent transversal problem in the class of infinite $K_n$-free graphs: we show that for any infinite $K_n$-free graph $G=(V,E)$ and $m\\in \\mathbb N$ there is a minimal $r=r(G,m)$ such that for any balanced $r$-colouring of the vertices of $G$ one can find an independent set which meets at least $m$ colour classes in a set of size $|V|$. Answering a conjecture of S. Thomass\\'e, we express the exact value of $r(H_n,m)$ (using Ramsey-numbers for finite digraphs), where $H_n$ is Henson's countable universal homogeneous $K_n$-free graph. In tu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06142","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":""},"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":"1611.06142","created_at":"2026-05-18T00:43:18.208367+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.06142v2","created_at":"2026-05-18T00:43:18.208367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06142","created_at":"2026-05-18T00:43:18.208367+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUKVCL5CYSKQ","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUKVCL5CYSKQDDQS","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUKVCL5C","created_at":"2026-05-18T12:30:19.053100+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/GUKVCL5CYSKQDDQSUS6HIE36T5","json":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5.json","graph_json":"https://pith.science/api/pith-number/GUKVCL5CYSKQDDQSUS6HIE36T5/graph.json","events_json":"https://pith.science/api/pith-number/GUKVCL5CYSKQDDQSUS6HIE36T5/events.json","paper":"https://pith.science/paper/GUKVCL5C"},"agent_actions":{"view_html":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5","download_json":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5.json","view_paper":"https://pith.science/paper/GUKVCL5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.06142&json=true","fetch_graph":"https://pith.science/api/pith-number/GUKVCL5CYSKQDDQSUS6HIE36T5/graph.json","fetch_events":"https://pith.science/api/pith-number/GUKVCL5CYSKQDDQSUS6HIE36T5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5/action/storage_attestation","attest_author":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5/action/author_attestation","sign_citation":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5/action/citation_signature","submit_replication":"https://pith.science/pith/GUKVCL5CYSKQDDQSUS6HIE36T5/action/replication_record"}},"created_at":"2026-05-18T00:43:18.208367+00:00","updated_at":"2026-05-18T00:43:18.208367+00:00"}