{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:YYYJG4SZ4O2QX2PJNYA4LAHLKZ","short_pith_number":"pith:YYYJG4SZ","schema_version":"1.0","canonical_sha256":"c630937259e3b50be9e96e01c580eb5667a2494a9baf33668d97cdeb03beef1b","source":{"kind":"arxiv","id":"2305.16760","version":2},"attestation_state":"computed","paper":{"title":"Transversals to colorful intersecting convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cuauhtemoc Gomez-Navarro, Edgardo Rold\\'an-Pensado","submitted_at":"2023-05-26T09:22:32Z","abstract_excerpt":"Let $K$ be a compact convex set in $\\mathbb{R}^2$ and let $\\mathcal{F}_1, \\mathcal{F}_2, \\mathcal{F}_3$ be finite families of translates of $K$ such that $A \\cap B \\neq \\emptyset$ for every $A \\in \\mathcal{F}_i$ and $B \\in \\mathcal{F}_j$ with $i \\neq j$. A conjecture by Dolnikov is that, under these conditions, there is always some $j \\in \\lbrace 1,2,3 \\rbrace$ such that $\\mathcal{F}_j$ can be pierced by $3$ points. In this paper we prove a stronger version of this conjecture when $K$ is a body of constant width or when it is close in Banach-Mazur distance to a disk. We also show that the conj"},"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":"2305.16760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-05-26T09:22:32Z","cross_cats_sorted":[],"title_canon_sha256":"49b018f351d07d0ccc1dd56672e90f943ecbdeceb459720487422eecb5349f80","abstract_canon_sha256":"d41fae7334376d5b586fa146dcc2e02be391fc325821c26393efc6cb9f61c159"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:22:05.714352Z","signature_b64":"w5cNFLbH91G4ff6/JmgwtZKRktUYArPE83DmQG/OqR0e+LbDZKrf2yc9AMzEObl177XLHBZ/SZ0ioCrh0lUzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c630937259e3b50be9e96e01c580eb5667a2494a9baf33668d97cdeb03beef1b","last_reissued_at":"2026-07-05T06:22:05.713931Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:22:05.713931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transversals to colorful intersecting convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cuauhtemoc Gomez-Navarro, Edgardo Rold\\'an-Pensado","submitted_at":"2023-05-26T09:22:32Z","abstract_excerpt":"Let $K$ be a compact convex set in $\\mathbb{R}^2$ and let $\\mathcal{F}_1, \\mathcal{F}_2, \\mathcal{F}_3$ be finite families of translates of $K$ such that $A \\cap B \\neq \\emptyset$ for every $A \\in \\mathcal{F}_i$ and $B \\in \\mathcal{F}_j$ with $i \\neq j$. A conjecture by Dolnikov is that, under these conditions, there is always some $j \\in \\lbrace 1,2,3 \\rbrace$ such that $\\mathcal{F}_j$ can be pierced by $3$ points. In this paper we prove a stronger version of this conjecture when $K$ is a body of constant width or when it is close in Banach-Mazur distance to a disk. We also show that the conj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16760","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.16760/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2305.16760","created_at":"2026-07-05T06:22:05.713989+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.16760v2","created_at":"2026-07-05T06:22:05.713989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16760","created_at":"2026-07-05T06:22:05.713989+00:00"},{"alias_kind":"pith_short_12","alias_value":"YYYJG4SZ4O2Q","created_at":"2026-07-05T06:22:05.713989+00:00"},{"alias_kind":"pith_short_16","alias_value":"YYYJG4SZ4O2QX2PJ","created_at":"2026-07-05T06:22:05.713989+00:00"},{"alias_kind":"pith_short_8","alias_value":"YYYJG4SZ","created_at":"2026-07-05T06:22:05.713989+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/YYYJG4SZ4O2QX2PJNYA4LAHLKZ","json":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ.json","graph_json":"https://pith.science/api/pith-number/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/graph.json","events_json":"https://pith.science/api/pith-number/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/events.json","paper":"https://pith.science/paper/YYYJG4SZ"},"agent_actions":{"view_html":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ","download_json":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ.json","view_paper":"https://pith.science/paper/YYYJG4SZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.16760&json=true","fetch_graph":"https://pith.science/api/pith-number/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/action/storage_attestation","attest_author":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/action/author_attestation","sign_citation":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/action/citation_signature","submit_replication":"https://pith.science/pith/YYYJG4SZ4O2QX2PJNYA4LAHLKZ/action/replication_record"}},"created_at":"2026-07-05T06:22:05.713989+00:00","updated_at":"2026-07-05T06:22:05.713989+00:00"}