{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JQDOQAFEWAJWUOIPJCY4SOQDAJ","short_pith_number":"pith:JQDOQAFE","schema_version":"1.0","canonical_sha256":"4c06e800a4b0136a390f48b1c93a03025dc99a80e9c04e2ace67b01a43bde3a8","source":{"kind":"arxiv","id":"1502.05332","version":1},"attestation_state":"computed","paper":{"title":"The number of non-crossing perfect plane matchings is minimized (almost) only by point sets in convex position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andrei Asinowski","submitted_at":"2015-02-18T18:33:18Z","abstract_excerpt":"It is well-known that the number of non-crossing perfect matchings of $2k$ points in convex position in the plane is $C_k$, the $k$th Catalan number. Garc\\'ia, Noy, and Tejel proved in 2000 that for any set of $2k$ points in general position, the number of such matchings is at least $C_k$. We show that the equality holds only for sets of points in convex position, and for one exceptional configuration of $6$ points."},"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":"1502.05332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-02-18T18:33:18Z","cross_cats_sorted":[],"title_canon_sha256":"96adc721a88da4e7af5fa550c141b1f3d7113ea6fd90497e4d3255024a4d3334","abstract_canon_sha256":"c0bd8d79a8448c25939b1c822372b33229bbba33efa06bb521fb4f5f2da12a56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:51.968879Z","signature_b64":"qpNRpHL7uT3M6AFvOtekeumJXhvM6HQ1/4hAJjPrz8KlbPSJdwiCuNCAi3nTG3MxVCaY91ljCipaM25Mk3K6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c06e800a4b0136a390f48b1c93a03025dc99a80e9c04e2ace67b01a43bde3a8","last_reissued_at":"2026-05-18T02:26:51.968448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:51.968448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of non-crossing perfect plane matchings is minimized (almost) only by point sets in convex position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andrei Asinowski","submitted_at":"2015-02-18T18:33:18Z","abstract_excerpt":"It is well-known that the number of non-crossing perfect matchings of $2k$ points in convex position in the plane is $C_k$, the $k$th Catalan number. Garc\\'ia, Noy, and Tejel proved in 2000 that for any set of $2k$ points in general position, the number of such matchings is at least $C_k$. We show that the equality holds only for sets of points in convex position, and for one exceptional configuration of $6$ points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05332","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":"1502.05332","created_at":"2026-05-18T02:26:51.968511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05332v1","created_at":"2026-05-18T02:26:51.968511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05332","created_at":"2026-05-18T02:26:51.968511+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQDOQAFEWAJW","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQDOQAFEWAJWUOIP","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQDOQAFE","created_at":"2026-05-18T12:29:27.538025+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/JQDOQAFEWAJWUOIPJCY4SOQDAJ","json":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ.json","graph_json":"https://pith.science/api/pith-number/JQDOQAFEWAJWUOIPJCY4SOQDAJ/graph.json","events_json":"https://pith.science/api/pith-number/JQDOQAFEWAJWUOIPJCY4SOQDAJ/events.json","paper":"https://pith.science/paper/JQDOQAFE"},"agent_actions":{"view_html":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ","download_json":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ.json","view_paper":"https://pith.science/paper/JQDOQAFE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05332&json=true","fetch_graph":"https://pith.science/api/pith-number/JQDOQAFEWAJWUOIPJCY4SOQDAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/JQDOQAFEWAJWUOIPJCY4SOQDAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ/action/storage_attestation","attest_author":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ/action/author_attestation","sign_citation":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ/action/citation_signature","submit_replication":"https://pith.science/pith/JQDOQAFEWAJWUOIPJCY4SOQDAJ/action/replication_record"}},"created_at":"2026-05-18T02:26:51.968511+00:00","updated_at":"2026-05-18T02:26:51.968511+00:00"}