{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LAZUOUW2IESHHHE2TDSZYMWYHA","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":"4a5d57b7dd512eb7ebea19b43612c42cfb3a955f4ecce96d55ae820b764137ac","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-01T07:48:19Z","title_canon_sha256":"1f6a6fed43d17e4f00003f90961f8f2bf243f8d61b876c7abe13a516ded89cc3"},"schema_version":"1.0","source":{"id":"1712.00220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00220","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00220v2","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00220","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"pith_short_12","alias_value":"LAZUOUW2IESH","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LAZUOUW2IESHHHE2","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LAZUOUW2","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:00ab06bf7b4f447b07f45ad0fcf0e3426c6b91cf34f711a265c128cd47247bf4","target":"graph","created_at":"2026-05-18T00:16:08Z","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":"Karasev conjectured that for any set of $3k$ lines in general position in the plane, which is partitioned into $3$ color classes of equal size $k$, the set can be partitioned into $k$ colorful 3-subsets such that all the triangles formed by the subsets have a point in common. Although the general conjecture is false, we show that Karasev's conjecture is true for lines in convex position. We also discuss possible generalizations of this result.","authors_text":"Kangmin Yoo, Seunghun Lee","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-01T07:48:19Z","title":"On a conjecture of Karasev"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00220","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:e9c9a173a7dd5c432a61bd5626bf84e83d767722cf072db8d85ad6d159a71585","target":"record","created_at":"2026-05-18T00:16:08Z","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":"4a5d57b7dd512eb7ebea19b43612c42cfb3a955f4ecce96d55ae820b764137ac","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-01T07:48:19Z","title_canon_sha256":"1f6a6fed43d17e4f00003f90961f8f2bf243f8d61b876c7abe13a516ded89cc3"},"schema_version":"1.0","source":{"id":"1712.00220","kind":"arxiv","version":2}},"canonical_sha256":"58334752da4124739c9a98e59c32d8381c8461f86641b289c57ef5d6ac211f58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58334752da4124739c9a98e59c32d8381c8461f86641b289c57ef5d6ac211f58","first_computed_at":"2026-05-18T00:16:08.247077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:08.247077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CZV+r4TRIAjWsZCcxwINPNJqSmlNNHOzVLD6vWvhCSfGR1lDFPl6kZ5EJFWbiFW9wX1QxpyPMWnkVwc894jQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:08.247808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9c9a173a7dd5c432a61bd5626bf84e83d767722cf072db8d85ad6d159a71585","sha256:00ab06bf7b4f447b07f45ad0fcf0e3426c6b91cf34f711a265c128cd47247bf4"],"state_sha256":"1ea88907d69ddec48f8c3b6c8ef4386cfe2a124a9673933687b7f994bad2ca2f"}