{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RH42ATTJSYRVWFSCL6JKHSCCPS","short_pith_number":"pith:RH42ATTJ","schema_version":"1.0","canonical_sha256":"89f9a04e6996235b16425f92a3c8427cb7a29ec0eb767737c4bc10238995a4e6","source":{"kind":"arxiv","id":"1803.06229","version":1},"attestation_state":"computed","paper":{"title":"Further Consequences of the Colorful Helly Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Edgardo Rold\\'an-Pensado, Leonardo Mart\\'inez-Sandoval, Natan Rubin","submitted_at":"2018-03-16T13:47:05Z","abstract_excerpt":"Let $\\mathcal{F}$ be a family of convex sets in ${\\mathbb R}^d$, which are colored with $d+1$ colors. We say that $\\mathcal{F}$ satisfies the Colorful Helly Property if every rainbow selection of $d+1$ sets, one set from each color class, has a non-empty common intersection. The Colorful Helly Theorem of Lov\\'asz states that for any such colorful family $\\mathcal{F}$ there is a color class $\\mathcal{F}_i\\subset \\mathcal{F}$, for $1\\leq i\\leq d+1$, whose sets have a non-empty intersection.\n  We establish further consequences of the Colorful Helly hypothesis. In particular, we show that for each"},"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":"1803.06229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-16T13:47:05Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"703b64e63c965a5e9add8890e11311e7a45a70f52af983bf07fa4355ef5dea51","abstract_canon_sha256":"ce22d674d2d550791a93fc4934b6edfce8c7ae5514c5543163bae44459f5d59a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:13.380444Z","signature_b64":"r30+vb6Kw9HPe5IPeOIc/hnfJzWKi+CrgLoJOcSR1M0aZS6WYHCByBKVVoSOYC4w4F55JcIxu9kvjOck5tsMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89f9a04e6996235b16425f92a3c8427cb7a29ec0eb767737c4bc10238995a4e6","last_reissued_at":"2026-05-18T00:20:13.379950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:13.379950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Further Consequences of the Colorful Helly Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Edgardo Rold\\'an-Pensado, Leonardo Mart\\'inez-Sandoval, Natan Rubin","submitted_at":"2018-03-16T13:47:05Z","abstract_excerpt":"Let $\\mathcal{F}$ be a family of convex sets in ${\\mathbb R}^d$, which are colored with $d+1$ colors. We say that $\\mathcal{F}$ satisfies the Colorful Helly Property if every rainbow selection of $d+1$ sets, one set from each color class, has a non-empty common intersection. The Colorful Helly Theorem of Lov\\'asz states that for any such colorful family $\\mathcal{F}$ there is a color class $\\mathcal{F}_i\\subset \\mathcal{F}$, for $1\\leq i\\leq d+1$, whose sets have a non-empty intersection.\n  We establish further consequences of the Colorful Helly hypothesis. In particular, we show that for each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06229","kind":"arxiv","version":1},"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":"1803.06229","created_at":"2026-05-18T00:20:13.380025+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.06229v1","created_at":"2026-05-18T00:20:13.380025+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06229","created_at":"2026-05-18T00:20:13.380025+00:00"},{"alias_kind":"pith_short_12","alias_value":"RH42ATTJSYRV","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RH42ATTJSYRVWFSC","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RH42ATTJ","created_at":"2026-05-18T12:32:50.500415+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/RH42ATTJSYRVWFSCL6JKHSCCPS","json":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS.json","graph_json":"https://pith.science/api/pith-number/RH42ATTJSYRVWFSCL6JKHSCCPS/graph.json","events_json":"https://pith.science/api/pith-number/RH42ATTJSYRVWFSCL6JKHSCCPS/events.json","paper":"https://pith.science/paper/RH42ATTJ"},"agent_actions":{"view_html":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS","download_json":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS.json","view_paper":"https://pith.science/paper/RH42ATTJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.06229&json=true","fetch_graph":"https://pith.science/api/pith-number/RH42ATTJSYRVWFSCL6JKHSCCPS/graph.json","fetch_events":"https://pith.science/api/pith-number/RH42ATTJSYRVWFSCL6JKHSCCPS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS/action/storage_attestation","attest_author":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS/action/author_attestation","sign_citation":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS/action/citation_signature","submit_replication":"https://pith.science/pith/RH42ATTJSYRVWFSCL6JKHSCCPS/action/replication_record"}},"created_at":"2026-05-18T00:20:13.380025+00:00","updated_at":"2026-05-18T00:20:13.380025+00:00"}