{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AFUAFKBDTNA3WDO3HUDDWL7WYY","short_pith_number":"pith:AFUAFKBD","schema_version":"1.0","canonical_sha256":"016802a8239b41bb0ddb3d063b2ff6c61e6abadaf83926735ed60640a848884d","source":{"kind":"arxiv","id":"1410.0258","version":4},"attestation_state":"computed","paper":{"title":"An abstract approach to polychromatic coloring: shallow hitting sets in ABA-free hypergraphs and pseudohalfplanes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi","submitted_at":"2014-10-01T15:18:22Z","abstract_excerpt":"The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic colorings using hypergraphs on ordered vertex sets. We introduce an abstract version of a framework by Smorodinsky and Yuditsky, used for polychromatic coloring halfplanes, and apply it to so-called ABA-free hypergraphs, which are a generalization of interval graphs. Using our methods, we prove that (2k-1)-uniform ABA-free hypergraphs have a polychromatic k-coloring, a problem posed by the second author. We also prove the same for hypergraphs defined on a point set by pseudohalfplanes. These res"},"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":"1410.0258","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-01T15:18:22Z","cross_cats_sorted":[],"title_canon_sha256":"e085ae7a4e5e3908cdbee9c3ab8d775c7de2aeec35a757bf8a15a894281a1e4b","abstract_canon_sha256":"f2a71bac1d08ac2f28a1ffe3a2ad427a6a8db1e24de4b70608c90c34574164c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:01.756434Z","signature_b64":"WKAHLDtx2K+GCLqfCY91/9yCkydkskLJUg+vcj306LqT8ve7m9NpmhpTPj6PNO5aDpIDKcchPsA2WX96q87ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"016802a8239b41bb0ddb3d063b2ff6c61e6abadaf83926735ed60640a848884d","last_reissued_at":"2026-05-17T23:53:01.755743Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:01.755743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An abstract approach to polychromatic coloring: shallow hitting sets in ABA-free hypergraphs and pseudohalfplanes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi","submitted_at":"2014-10-01T15:18:22Z","abstract_excerpt":"The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic colorings using hypergraphs on ordered vertex sets. We introduce an abstract version of a framework by Smorodinsky and Yuditsky, used for polychromatic coloring halfplanes, and apply it to so-called ABA-free hypergraphs, which are a generalization of interval graphs. Using our methods, we prove that (2k-1)-uniform ABA-free hypergraphs have a polychromatic k-coloring, a problem posed by the second author. We also prove the same for hypergraphs defined on a point set by pseudohalfplanes. These res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0258","kind":"arxiv","version":4},"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":"1410.0258","created_at":"2026-05-17T23:53:01.755866+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.0258v4","created_at":"2026-05-17T23:53:01.755866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0258","created_at":"2026-05-17T23:53:01.755866+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFUAFKBDTNA3","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFUAFKBDTNA3WDO3","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFUAFKBD","created_at":"2026-05-18T12:28:19.803747+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/AFUAFKBDTNA3WDO3HUDDWL7WYY","json":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY.json","graph_json":"https://pith.science/api/pith-number/AFUAFKBDTNA3WDO3HUDDWL7WYY/graph.json","events_json":"https://pith.science/api/pith-number/AFUAFKBDTNA3WDO3HUDDWL7WYY/events.json","paper":"https://pith.science/paper/AFUAFKBD"},"agent_actions":{"view_html":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY","download_json":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY.json","view_paper":"https://pith.science/paper/AFUAFKBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.0258&json=true","fetch_graph":"https://pith.science/api/pith-number/AFUAFKBDTNA3WDO3HUDDWL7WYY/graph.json","fetch_events":"https://pith.science/api/pith-number/AFUAFKBDTNA3WDO3HUDDWL7WYY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY/action/storage_attestation","attest_author":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY/action/author_attestation","sign_citation":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY/action/citation_signature","submit_replication":"https://pith.science/pith/AFUAFKBDTNA3WDO3HUDDWL7WYY/action/replication_record"}},"created_at":"2026-05-17T23:53:01.755866+00:00","updated_at":"2026-05-17T23:53:01.755866+00:00"}