{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RH42ATTJSYRVWFSCL6JKHSCCPS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ce22d674d2d550791a93fc4934b6edfce8c7ae5514c5543163bae44459f5d59a","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-16T13:47:05Z","title_canon_sha256":"703b64e63c965a5e9add8890e11311e7a45a70f52af983bf07fa4355ef5dea51"},"schema_version":"1.0","source":{"id":"1803.06229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06229","created_at":"2026-05-18T00:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06229v1","created_at":"2026-05-18T00:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06229","created_at":"2026-05-18T00:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"RH42ATTJSYRV","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RH42ATTJSYRVWFSC","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RH42ATTJ","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:e42b0302226f981b950ce897200c6cec9fa432b021e2d3bae7c2648c06b68ac0","target":"graph","created_at":"2026-05-18T00:20:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Edgardo Rold\\'an-Pensado, Leonardo Mart\\'inez-Sandoval, Natan Rubin","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-16T13:47:05Z","title":"Further Consequences of the Colorful Helly Hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06229","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:26dd2f03a6853e301df5589f933536bf75fa5da3accaed34ea880ae392e99a4e","target":"record","created_at":"2026-05-18T00:20:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ce22d674d2d550791a93fc4934b6edfce8c7ae5514c5543163bae44459f5d59a","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-16T13:47:05Z","title_canon_sha256":"703b64e63c965a5e9add8890e11311e7a45a70f52af983bf07fa4355ef5dea51"},"schema_version":"1.0","source":{"id":"1803.06229","kind":"arxiv","version":1}},"canonical_sha256":"89f9a04e6996235b16425f92a3c8427cb7a29ec0eb767737c4bc10238995a4e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89f9a04e6996235b16425f92a3c8427cb7a29ec0eb767737c4bc10238995a4e6","first_computed_at":"2026-05-18T00:20:13.379950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:13.379950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r30+vb6Kw9HPe5IPeOIc/hnfJzWKi+CrgLoJOcSR1M0aZS6WYHCByBKVVoSOYC4w4F55JcIxu9kvjOck5tsMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:13.380444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26dd2f03a6853e301df5589f933536bf75fa5da3accaed34ea880ae392e99a4e","sha256:e42b0302226f981b950ce897200c6cec9fa432b021e2d3bae7c2648c06b68ac0"],"state_sha256":"b4b51cd3b45d11264c53cc1417bd8f832c8cc2d78ff3ea86a5cf4956b06e51f2"}