{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FYBF6ISYCRKLZXFO7OLKJ3THS5","short_pith_number":"pith:FYBF6ISY","schema_version":"1.0","canonical_sha256":"2e025f22581454bcdcaefb96a4ee67975745b874f5c6e767a442ae8934e1484b","source":{"kind":"arxiv","id":"1307.0909","version":2},"attestation_state":"computed","paper":{"title":"Regular systems of paths and families of convex sets in convex position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Alfredo Hubard, Andreas F. Holmsen, Michael G. Dobbins","submitted_at":"2013-07-03T03:55:49Z","abstract_excerpt":"In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five is in convex position. (If each pair of bodies have at most two common tangents it is enough to assume that every triple is in convex position, and likewise, if each pair of bodies have at most four common tangents it is enough to assume that every quadruple is in convex position.) This confirms a conjecture of Pach and Toth, and generalizes a theorem of Bi"},"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":"1307.0909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-07-03T03:55:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b084945b1420b7328657779e5d96f309d4c055e4c4c47b7d8e1b40757b2b7d9b","abstract_canon_sha256":"1f2b2a3bbde720763c8f4decec4177a72843fb2559db22717255de9357f619b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:37.888882Z","signature_b64":"X/N0x8v7jWHpvbjWosKjrYWn5D4L7k/SvWBYWCB8AQYuB200ANQvGvmGdlteK2uTkmxIAVCgQCrR33caoeioBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e025f22581454bcdcaefb96a4ee67975745b874f5c6e767a442ae8934e1484b","last_reissued_at":"2026-05-18T02:54:37.888376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:37.888376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regular systems of paths and families of convex sets in convex position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Alfredo Hubard, Andreas F. Holmsen, Michael G. Dobbins","submitted_at":"2013-07-03T03:55:49Z","abstract_excerpt":"In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five is in convex position. (If each pair of bodies have at most two common tangents it is enough to assume that every triple is in convex position, and likewise, if each pair of bodies have at most four common tangents it is enough to assume that every quadruple is in convex position.) This confirms a conjecture of Pach and Toth, and generalizes a theorem of Bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0909","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":"1307.0909","created_at":"2026-05-18T02:54:37.888458+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0909v2","created_at":"2026-05-18T02:54:37.888458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0909","created_at":"2026-05-18T02:54:37.888458+00:00"},{"alias_kind":"pith_short_12","alias_value":"FYBF6ISYCRKL","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FYBF6ISYCRKLZXFO","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FYBF6ISY","created_at":"2026-05-18T12:27:45.050594+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/FYBF6ISYCRKLZXFO7OLKJ3THS5","json":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5.json","graph_json":"https://pith.science/api/pith-number/FYBF6ISYCRKLZXFO7OLKJ3THS5/graph.json","events_json":"https://pith.science/api/pith-number/FYBF6ISYCRKLZXFO7OLKJ3THS5/events.json","paper":"https://pith.science/paper/FYBF6ISY"},"agent_actions":{"view_html":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5","download_json":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5.json","view_paper":"https://pith.science/paper/FYBF6ISY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0909&json=true","fetch_graph":"https://pith.science/api/pith-number/FYBF6ISYCRKLZXFO7OLKJ3THS5/graph.json","fetch_events":"https://pith.science/api/pith-number/FYBF6ISYCRKLZXFO7OLKJ3THS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5/action/storage_attestation","attest_author":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5/action/author_attestation","sign_citation":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5/action/citation_signature","submit_replication":"https://pith.science/pith/FYBF6ISYCRKLZXFO7OLKJ3THS5/action/replication_record"}},"created_at":"2026-05-18T02:54:37.888458+00:00","updated_at":"2026-05-18T02:54:37.888458+00:00"}