{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UP5PRFSGUT6FR44J7ZV3HFCLLN","short_pith_number":"pith:UP5PRFSG","schema_version":"1.0","canonical_sha256":"a3faf89646a4fc58f389fe6bb3944b5b5a83ba1eb0947c46edb65950480dd1b3","source":{"kind":"arxiv","id":"1807.02384","version":1},"attestation_state":"computed","paper":{"title":"Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CO","authors_text":"David Cushing, Florentin M\\\"unch, Jack Koolen, Norbert Peyerimhoff, Shiping Liu, Supanat Kamtue","submitted_at":"2018-07-06T12:45:51Z","abstract_excerpt":"We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cubes, Johnson graphs $J(2n,n)$, the Gosset graph and suitable Cartesian products). We also present a purely combinatorial reformulation of this result. We show that Bonnet-Myers sharpness implies Lichnerowicz sharpness. We also relate Bonnet-Myers sharpness to an upper bound of Bakry-\\'Emery $\\infty$-curvature, which motivates a generalconjecture abo"},"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":"1807.02384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-06T12:45:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"e4e19a1a0a051ad6bf86834f438c313811d2663433b518407247e81f24fc3929","abstract_canon_sha256":"866e5de065f1e00acecf094e9d9d7c914c0f1653f76234f2decb45001ef389ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:22.240243Z","signature_b64":"8r3V4zmQNXosEPytkZmnkMIkRkzfEeorO/zuLz1F3DSqNvxlvKtbaUVEL+q6uCOgRlBnl0exFkdvTsvIfI0LDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3faf89646a4fc58f389fe6bb3944b5b5a83ba1eb0947c46edb65950480dd1b3","last_reissued_at":"2026-05-18T00:11:22.239532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:22.239532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CO","authors_text":"David Cushing, Florentin M\\\"unch, Jack Koolen, Norbert Peyerimhoff, Shiping Liu, Supanat Kamtue","submitted_at":"2018-07-06T12:45:51Z","abstract_excerpt":"We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cubes, Johnson graphs $J(2n,n)$, the Gosset graph and suitable Cartesian products). We also present a purely combinatorial reformulation of this result. We show that Bonnet-Myers sharpness implies Lichnerowicz sharpness. We also relate Bonnet-Myers sharpness to an upper bound of Bakry-\\'Emery $\\infty$-curvature, which motivates a generalconjecture abo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02384","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":"1807.02384","created_at":"2026-05-18T00:11:22.239647+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.02384v1","created_at":"2026-05-18T00:11:22.239647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02384","created_at":"2026-05-18T00:11:22.239647+00:00"},{"alias_kind":"pith_short_12","alias_value":"UP5PRFSGUT6F","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UP5PRFSGUT6FR44J","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UP5PRFSG","created_at":"2026-05-18T12:32:56.356000+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/UP5PRFSGUT6FR44J7ZV3HFCLLN","json":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN.json","graph_json":"https://pith.science/api/pith-number/UP5PRFSGUT6FR44J7ZV3HFCLLN/graph.json","events_json":"https://pith.science/api/pith-number/UP5PRFSGUT6FR44J7ZV3HFCLLN/events.json","paper":"https://pith.science/paper/UP5PRFSG"},"agent_actions":{"view_html":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN","download_json":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN.json","view_paper":"https://pith.science/paper/UP5PRFSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.02384&json=true","fetch_graph":"https://pith.science/api/pith-number/UP5PRFSGUT6FR44J7ZV3HFCLLN/graph.json","fetch_events":"https://pith.science/api/pith-number/UP5PRFSGUT6FR44J7ZV3HFCLLN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN/action/storage_attestation","attest_author":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN/action/author_attestation","sign_citation":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN/action/citation_signature","submit_replication":"https://pith.science/pith/UP5PRFSGUT6FR44J7ZV3HFCLLN/action/replication_record"}},"created_at":"2026-05-18T00:11:22.239647+00:00","updated_at":"2026-05-18T00:11:22.239647+00:00"}