{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7GA7VYM6K2AD6N6RIOVMB4ATM5","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":"e9574ee3501ae7d8117aa054a6601a0302b00692c4251d0924e04fff21aa941b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-24T20:33:20Z","title_canon_sha256":"5e734c2b30ae3ef90a7565663687d42599fe15c570510228805a9d87cf4a8a09"},"schema_version":"1.0","source":{"id":"1805.09888","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09888","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09888v2","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09888","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"7GA7VYM6K2AD","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7GA7VYM6K2AD6N6R","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7GA7VYM6","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:d90420378207d3ca748d053c1edaf40d3c76550c0914bbe0a365beb34fffd2fa","target":"graph","created_at":"2026-05-17T23:49:22Z","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":"A crossing family is a collection of pairwise crossing segments, this concept was introduced by Aronov et. al. (1994). They prove that any set of $n$ points (in general position) in the plain contains a crossing family of size $\\sqrt{n/12}$. In this paper we present a generalization of the concept and give several results regarding this generalization.","authors_text":"Christian Rubio-Montiel, Dolores Lara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-24T20:33:20Z","title":"On crossing families of complete geometric graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09888","kind":"arxiv","version":2},"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":"sha256:716d76655e8c7a190cf15791618f05aff7daa5e384d85ad2e1fdf36bc1465a35","target":"record","created_at":"2026-05-17T23:49:22Z","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":"e9574ee3501ae7d8117aa054a6601a0302b00692c4251d0924e04fff21aa941b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-24T20:33:20Z","title_canon_sha256":"5e734c2b30ae3ef90a7565663687d42599fe15c570510228805a9d87cf4a8a09"},"schema_version":"1.0","source":{"id":"1805.09888","kind":"arxiv","version":2}},"canonical_sha256":"f981fae19e56803f37d143aac0f013677b837ce5b403030f0e9ad5f744cfe4c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f981fae19e56803f37d143aac0f013677b837ce5b403030f0e9ad5f744cfe4c6","first_computed_at":"2026-05-17T23:49:22.462101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:22.462101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1gt4Mr2ClJ109Pv7hfbSGbuzEzJx+F4iTFolwNwGTFlxV1RH+Pw8zarzSFQGsASVeQeVZCNjA8Tlgw4y20+0CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:22.462753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09888","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:716d76655e8c7a190cf15791618f05aff7daa5e384d85ad2e1fdf36bc1465a35","sha256:d90420378207d3ca748d053c1edaf40d3c76550c0914bbe0a365beb34fffd2fa"],"state_sha256":"466f4cf7d70c51589b63f3e2163f2420d718343ac3594982655f886427f582ac"}