{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ABDVSHQEFIEQ5MINZX6V6Z6K6K","short_pith_number":"pith:ABDVSHQE","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"},"canonical_sha256":"0047591e042a090eb10dcdfd5f67caf28b380178bbe01f1e25bdfd64d2ec2fc3","source":{"kind":"arxiv","id":"2409.13666","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.13666","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"2409.13666v1","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.13666","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"ABDVSHQEFIEQ","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"pith_short_16","alias_value":"ABDVSHQEFIEQ5MIN","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"pith_short_8","alias_value":"ABDVSHQE","created_at":"2026-07-05T09:09:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ABDVSHQEFIEQ5MINZX6V6Z6K6K","target":"record","payload":{"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"},"canonical_sha256":"0047591e042a090eb10dcdfd5f67caf28b380178bbe01f1e25bdfd64d2ec2fc3","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"},"source_kind":"arxiv","source_id":"2409.13666","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:09:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WNUGKcz1fvBLKpYi8gBUiuN8hSMgAz23Ifd8bXAJ6jFbsFXdNnvEN7ophWp7ABrUCIrixGfr27igINQkxolmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T15:15:30.242594Z"},"content_sha256":"d70ac90d1e7c50a9ca7bdcf859df5403b10a0d271e4700d494fb1f5802eb2ab4","schema_version":"1.0","event_id":"sha256:d70ac90d1e7c50a9ca7bdcf859df5403b10a0d271e4700d494fb1f5802eb2ab4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ABDVSHQEFIEQ5MINZX6V6Z6K6K","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:09:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h4aT2iXc4/7jSCzLStleAIRsWczgmEe8oxTCUP1YbozACNMldX7ux48q6d+sXxCCiW51VOZypzMijRFuCxaUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T15:15:30.243145Z"},"content_sha256":"fb6d5e6ee86600aa09430305ab9ec70a80212c784f789d7e80518a889177cfa1","schema_version":"1.0","event_id":"sha256:fb6d5e6ee86600aa09430305ab9ec70a80212c784f789d7e80518a889177cfa1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/bundle.json","state_url":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-31T15:15:30Z","links":{"resolver":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K","bundle":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/bundle.json","state":"https://pith.science/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABDVSHQEFIEQ5MINZX6V6Z6K6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ABDVSHQEFIEQ5MINZX6V6Z6K6K","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":"8f06fd413761cfe4cff19dd60c0a5e086afaac6158390ca85d3921ceaee865fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-20T17:21:02Z","title_canon_sha256":"cb962c1098c3b81a4a20efac88d8d4e6a5ee0b0b8b94dceea64614ff43241df8"},"schema_version":"1.0","source":{"id":"2409.13666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.13666","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"2409.13666v1","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.13666","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"ABDVSHQEFIEQ","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"pith_short_16","alias_value":"ABDVSHQEFIEQ5MIN","created_at":"2026-07-05T09:09:47Z"},{"alias_kind":"pith_short_8","alias_value":"ABDVSHQE","created_at":"2026-07-05T09:09:47Z"}],"graph_snapshots":[{"event_id":"sha256:fb6d5e6ee86600aa09430305ab9ec70a80212c784f789d7e80518a889177cfa1","target":"graph","created_at":"2026-07-05T09:09:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.13666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Linyuan Lu, Xiaonan Liu, Zhiyu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-20T17:21:02Z","title":"On the size of outerplanar graphs with positive Lin-Lu-Yau Ricci curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13666","kind":"arxiv","version":1},"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:d70ac90d1e7c50a9ca7bdcf859df5403b10a0d271e4700d494fb1f5802eb2ab4","target":"record","created_at":"2026-07-05T09:09:47Z","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":"8f06fd413761cfe4cff19dd60c0a5e086afaac6158390ca85d3921ceaee865fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-20T17:21:02Z","title_canon_sha256":"cb962c1098c3b81a4a20efac88d8d4e6a5ee0b0b8b94dceea64614ff43241df8"},"schema_version":"1.0","source":{"id":"2409.13666","kind":"arxiv","version":1}},"canonical_sha256":"0047591e042a090eb10dcdfd5f67caf28b380178bbe01f1e25bdfd64d2ec2fc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0047591e042a090eb10dcdfd5f67caf28b380178bbe01f1e25bdfd64d2ec2fc3","first_computed_at":"2026-07-05T09:09:47.002008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:47.002008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tCYJczffTKBDs0Lbo8kcEm0MxN24pDKjUWjUeOThszaf5j1BVh5SLHYv1Neohbvqy7saU8Kv7ZVE7KQ7qiHyBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:47.002492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.13666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d70ac90d1e7c50a9ca7bdcf859df5403b10a0d271e4700d494fb1f5802eb2ab4","sha256:fb6d5e6ee86600aa09430305ab9ec70a80212c784f789d7e80518a889177cfa1"],"state_sha256":"d5c61e1c5053ec9dd4a076a755ac975bbf464a3236d2acdff59b8e46175d8fda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTdtqN3ORSKDSuCpdqCmGmyMIf81bdeLC0tZGJ7W35UtLSPY8DqDco/Jor6x83B/M7d5N15frTfn8CbaYbKyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T15:15:30.246672Z","bundle_sha256":"71928d6217a66b26d6ee4a0d935006e3687b76db9866c2c151fc57f7a99ca5f5"}}