{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XHWJJ7NVQDEBHYFIVQ4RDKFOQH","short_pith_number":"pith:XHWJJ7NV","schema_version":"1.0","canonical_sha256":"b9ec94fdb580c813e0a8ac3911a8ae81d9556ce5a9f72814992988b2b7e48f2d","source":{"kind":"arxiv","id":"1711.05473","version":2},"attestation_state":"computed","paper":{"title":"Coloring intersection hypergraphs of pseudo-disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh","submitted_at":"2017-11-15T09:38:30Z","abstract_excerpt":"We prove that the intersection hypergraph of a family of $n$ pseudo-disks with respect to another family of pseudo-disks admits a proper coloring with $4$ colors and a conflict-free coloring with $O(\\log n)$ colors. Along the way we prove that the respective Delaunay-graph is planar. We also prove that the intersection hypergraph of a family of $n$ regions with linear union complexity with respect to a family of pseudo-disks admits a proper coloring with constantly many colors and a conflict-free coloring with $O(\\log n)$ colors. Our results serve as a common generalization and strengthening o"},"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":"1711.05473","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-15T09:38:30Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"fbd202b0c69ff7c8c79e0bc941006cce8de945121fa69a4517f8335217754dfd","abstract_canon_sha256":"f23c5eb1540b5c092d602aca1d1a8aee738b3233767e84890a2a48bee77469de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:32.496164Z","signature_b64":"jILHMDHrCaLawYVRokbh7JU4wQY27oMV2a2VefzkgxhQYZGftqcMgqFMiPJNpZ5cqJ+PjDjf2d7MSBdV9uxXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9ec94fdb580c813e0a8ac3911a8ae81d9556ce5a9f72814992988b2b7e48f2d","last_reissued_at":"2026-05-18T00:05:32.495707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:32.495707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coloring intersection hypergraphs of pseudo-disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh","submitted_at":"2017-11-15T09:38:30Z","abstract_excerpt":"We prove that the intersection hypergraph of a family of $n$ pseudo-disks with respect to another family of pseudo-disks admits a proper coloring with $4$ colors and a conflict-free coloring with $O(\\log n)$ colors. Along the way we prove that the respective Delaunay-graph is planar. We also prove that the intersection hypergraph of a family of $n$ regions with linear union complexity with respect to a family of pseudo-disks admits a proper coloring with constantly many colors and a conflict-free coloring with $O(\\log n)$ colors. Our results serve as a common generalization and strengthening o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05473","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":"1711.05473","created_at":"2026-05-18T00:05:32.495767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05473v2","created_at":"2026-05-18T00:05:32.495767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05473","created_at":"2026-05-18T00:05:32.495767+00:00"},{"alias_kind":"pith_short_12","alias_value":"XHWJJ7NVQDEB","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XHWJJ7NVQDEBHYFI","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XHWJJ7NV","created_at":"2026-05-18T12:31:53.515858+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/XHWJJ7NVQDEBHYFIVQ4RDKFOQH","json":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH.json","graph_json":"https://pith.science/api/pith-number/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/graph.json","events_json":"https://pith.science/api/pith-number/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/events.json","paper":"https://pith.science/paper/XHWJJ7NV"},"agent_actions":{"view_html":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH","download_json":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH.json","view_paper":"https://pith.science/paper/XHWJJ7NV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05473&json=true","fetch_graph":"https://pith.science/api/pith-number/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/graph.json","fetch_events":"https://pith.science/api/pith-number/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/action/storage_attestation","attest_author":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/action/author_attestation","sign_citation":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/action/citation_signature","submit_replication":"https://pith.science/pith/XHWJJ7NVQDEBHYFIVQ4RDKFOQH/action/replication_record"}},"created_at":"2026-05-18T00:05:32.495767+00:00","updated_at":"2026-05-18T00:05:32.495767+00:00"}