{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ABDVSHQEFIEQ5MINZX6V6Z6K6K","short_pith_number":"pith:ABDVSHQE","schema_version":"1.0","canonical_sha256":"0047591e042a090eb10dcdfd5f67caf28b380178bbe01f1e25bdfd64d2ec2fc3","source":{"kind":"arxiv","id":"2409.13666","version":1},"attestation_state":"computed","paper":{"title":"On the size of outerplanar graphs with positive Lin-Lu-Yau Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Linyuan Lu, Xiaonan Liu, Zhiyu Wang","submitted_at":"2024-09-20T17:21:02Z","abstract_excerpt":"In this paper, extending a result of Brooks et.al. [arXiv:2403.04110], we show that if an outerplanar graph $G$ with minimum degree at least $2$ has positive Lin-Lu-Yau curvature on every vertex pair, then $G$ has at most $10$ vertices, and this upper bound is sharp."},"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":"2409.13666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-20T17:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"cb962c1098c3b81a4a20efac88d8d4e6a5ee0b0b8b94dceea64614ff43241df8","abstract_canon_sha256":"8f06fd413761cfe4cff19dd60c0a5e086afaac6158390ca85d3921ceaee865fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:47.002492Z","signature_b64":"tCYJczffTKBDs0Lbo8kcEm0MxN24pDKjUWjUeOThszaf5j1BVh5SLHYv1Neohbvqy7saU8Kv7ZVE7KQ7qiHyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0047591e042a090eb10dcdfd5f67caf28b380178bbe01f1e25bdfd64d2ec2fc3","last_reissued_at":"2026-07-05T09:09:47.002008Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:47.002008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the size of outerplanar graphs with positive Lin-Lu-Yau Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Linyuan Lu, Xiaonan Liu, Zhiyu Wang","submitted_at":"2024-09-20T17:21:02Z","abstract_excerpt":"In this paper, extending a result of Brooks et.al. [arXiv:2403.04110], we show that if an outerplanar graph $G$ with minimum degree at least $2$ has positive Lin-Lu-Yau curvature on every vertex pair, then $G$ has at most $10$ vertices, and this upper bound is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13666","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.13666/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2409.13666","created_at":"2026-07-05T09:09:47.002077+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.13666v1","created_at":"2026-07-05T09:09:47.002077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.13666","created_at":"2026-07-05T09:09:47.002077+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABDVSHQEFIEQ","created_at":"2026-07-05T09:09:47.002077+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABDVSHQEFIEQ5MIN","created_at":"2026-07-05T09:09:47.002077+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABDVSHQE","created_at":"2026-07-05T09:09:47.002077+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/ABDVSHQEFIEQ5MINZX6V6Z6K6K","json":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K.json","graph_json":"https://pith.science/api/pith-number/ABDVSHQEFIEQ5MINZX6V6Z6K6K/graph.json","events_json":"https://pith.science/api/pith-number/ABDVSHQEFIEQ5MINZX6V6Z6K6K/events.json","paper":"https://pith.science/paper/ABDVSHQE"},"agent_actions":{"view_html":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K","download_json":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K.json","view_paper":"https://pith.science/paper/ABDVSHQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.13666&json=true","fetch_graph":"https://pith.science/api/pith-number/ABDVSHQEFIEQ5MINZX6V6Z6K6K/graph.json","fetch_events":"https://pith.science/api/pith-number/ABDVSHQEFIEQ5MINZX6V6Z6K6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/action/storage_attestation","attest_author":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/action/author_attestation","sign_citation":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/action/citation_signature","submit_replication":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/action/replication_record"}},"created_at":"2026-07-05T09:09:47.002077+00:00","updated_at":"2026-07-05T09:09:47.002077+00:00"}