{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6ZPAHK3TFBQ63Z5WWE34UDZ7UE","short_pith_number":"pith:6ZPAHK3T","schema_version":"1.0","canonical_sha256":"f65e03ab732861ede7b6b137ca0f3fa10263acda493576a6b22e33676b2e0ae2","source":{"kind":"arxiv","id":"1712.07421","version":2},"attestation_state":"computed","paper":{"title":"Rainbow cycles in flip graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Leon Sering, Linda Kleist, Stefan Felsner, Torsten M\\\"utze","submitted_at":"2017-12-20T11:28:07Z","abstract_excerpt":"The flip graph of triangulations has as vertices all triangulations of a convex $n$-gon, and an edge between any two triangulations that differ in exactly one edge. An $r$-rainbow cycle in this graph is a cycle in which every inner edge of the triangulation appears exactly $r$ times. This notion of a rainbow cycle extends in a natural way to other flip graphs. In this paper we investigate the existence of $r$-rainbow cycles for three different flip graphs on classes of geometric objects: the aforementioned flip graph of triangulations of a convex $n$-gon, the flip graph of plane trees on an ar"},"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":"1712.07421","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-20T11:28:07Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"147d2703f8fda2e393198c43bd3a156e28a432eaaf8b112d9bf4a9c24b98ab60","abstract_canon_sha256":"caf1fddc79afba91f825921c2f7139a46e7d01fe02b00112c8fb3a65ffb90c47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:23.499038Z","signature_b64":"2Cj067+rTMFiIFVDwfCa0ZpQjnObSu5e3rOjN8KnbrL6yXP7Cq7rrB502wlAqRid+MFIrABF8LPkE/JqtFA7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f65e03ab732861ede7b6b137ca0f3fa10263acda493576a6b22e33676b2e0ae2","last_reissued_at":"2026-05-18T00:01:23.498649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:23.498649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rainbow cycles in flip graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Leon Sering, Linda Kleist, Stefan Felsner, Torsten M\\\"utze","submitted_at":"2017-12-20T11:28:07Z","abstract_excerpt":"The flip graph of triangulations has as vertices all triangulations of a convex $n$-gon, and an edge between any two triangulations that differ in exactly one edge. An $r$-rainbow cycle in this graph is a cycle in which every inner edge of the triangulation appears exactly $r$ times. This notion of a rainbow cycle extends in a natural way to other flip graphs. In this paper we investigate the existence of $r$-rainbow cycles for three different flip graphs on classes of geometric objects: the aforementioned flip graph of triangulations of a convex $n$-gon, the flip graph of plane trees on an ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07421","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":""},"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":"1712.07421","created_at":"2026-05-18T00:01:23.498706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.07421v2","created_at":"2026-05-18T00:01:23.498706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07421","created_at":"2026-05-18T00:01:23.498706+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ZPAHK3TFBQ6","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ZPAHK3TFBQ63Z5W","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ZPAHK3T","created_at":"2026-05-18T12:31:03.183658+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/6ZPAHK3TFBQ63Z5WWE34UDZ7UE","json":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE.json","graph_json":"https://pith.science/api/pith-number/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/graph.json","events_json":"https://pith.science/api/pith-number/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/events.json","paper":"https://pith.science/paper/6ZPAHK3T"},"agent_actions":{"view_html":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE","download_json":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE.json","view_paper":"https://pith.science/paper/6ZPAHK3T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.07421&json=true","fetch_graph":"https://pith.science/api/pith-number/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/graph.json","fetch_events":"https://pith.science/api/pith-number/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/action/storage_attestation","attest_author":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/action/author_attestation","sign_citation":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/action/citation_signature","submit_replication":"https://pith.science/pith/6ZPAHK3TFBQ63Z5WWE34UDZ7UE/action/replication_record"}},"created_at":"2026-05-18T00:01:23.498706+00:00","updated_at":"2026-05-18T00:01:23.498706+00:00"}