{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MCA4YMFKNWABPXUIGX5FUJ35CP","short_pith_number":"pith:MCA4YMFK","schema_version":"1.0","canonical_sha256":"6081cc30aa6d8017de8835fa5a277d13e64a143ed40f475778a87ecf181a4455","source":{"kind":"arxiv","id":"1503.01669","version":2},"attestation_state":"computed","paper":{"title":"More on Decomposing Coverings by Octants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi","submitted_at":"2015-03-05T15:48:15Z","abstract_excerpt":"In this note we improve our upper bound given earlier by showing that every 9-fold covering of a point set in the space by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering that does not decompose into two coverings. The same bounds also hold for coverings of points in $\\R^2$ by finitely many homothets or translates of a triangle. We also prove that certain dynamic interval coloring problems are equivalent to the above question."},"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":"1503.01669","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-05T15:48:15Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"acdc26f4ed52c45ac7c1909e20c1e4f88fe375198d4bdc88cba252e63e56972b","abstract_canon_sha256":"df626a8cb2679e6f0d0c7bfebb2896e09813ef77e91dcc2657e5b016b7db30f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:43.299093Z","signature_b64":"fQIb75xT2TvSGPfyVqiGGGTpe1wFbQjZb6M2T15cQVD8fpcxqVwuzXJ2zrZCRAZGvdxFNxmTD3CYbre6at4XDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6081cc30aa6d8017de8835fa5a277d13e64a143ed40f475778a87ecf181a4455","last_reissued_at":"2026-05-18T01:26:43.298329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:43.298329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"More on Decomposing Coverings by Octants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi","submitted_at":"2015-03-05T15:48:15Z","abstract_excerpt":"In this note we improve our upper bound given earlier by showing that every 9-fold covering of a point set in the space by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering that does not decompose into two coverings. The same bounds also hold for coverings of points in $\\R^2$ by finitely many homothets or translates of a triangle. We also prove that certain dynamic interval coloring problems are equivalent to the above question."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01669","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":"1503.01669","created_at":"2026-05-18T01:26:43.298454+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01669v2","created_at":"2026-05-18T01:26:43.298454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01669","created_at":"2026-05-18T01:26:43.298454+00:00"},{"alias_kind":"pith_short_12","alias_value":"MCA4YMFKNWAB","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MCA4YMFKNWABPXUI","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MCA4YMFK","created_at":"2026-05-18T12:29:32.376354+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/MCA4YMFKNWABPXUIGX5FUJ35CP","json":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP.json","graph_json":"https://pith.science/api/pith-number/MCA4YMFKNWABPXUIGX5FUJ35CP/graph.json","events_json":"https://pith.science/api/pith-number/MCA4YMFKNWABPXUIGX5FUJ35CP/events.json","paper":"https://pith.science/paper/MCA4YMFK"},"agent_actions":{"view_html":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP","download_json":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP.json","view_paper":"https://pith.science/paper/MCA4YMFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01669&json=true","fetch_graph":"https://pith.science/api/pith-number/MCA4YMFKNWABPXUIGX5FUJ35CP/graph.json","fetch_events":"https://pith.science/api/pith-number/MCA4YMFKNWABPXUIGX5FUJ35CP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP/action/storage_attestation","attest_author":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP/action/author_attestation","sign_citation":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP/action/citation_signature","submit_replication":"https://pith.science/pith/MCA4YMFKNWABPXUIGX5FUJ35CP/action/replication_record"}},"created_at":"2026-05-18T01:26:43.298454+00:00","updated_at":"2026-05-18T01:26:43.298454+00:00"}