{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:DINOFY6OR3XUROPDQLZS6LBH6L","short_pith_number":"pith:DINOFY6O","schema_version":"1.0","canonical_sha256":"1a1ae2e3ce8eef48b9e382f32f2c27f2d79a3e1d3321e616750d1a7137c04cf1","source":{"kind":"arxiv","id":"1012.2632","version":1},"attestation_state":"computed","paper":{"title":"There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Greg Markowsky, Jack H. Koolen, Jongyook Park","submitted_at":"2010-12-13T05:16:45Z","abstract_excerpt":"In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2/k<=C. This extends a conjecture of Bannai and Ito."},"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":"1012.2632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-13T05:16:45Z","cross_cats_sorted":[],"title_canon_sha256":"bc5c9f867c501a1bc168b938c863ec212cd12a74ff5eaf0fc5447363a3ef0e2a","abstract_canon_sha256":"7a5ae2b9142aac85bf2bf3a544ede06bd8793195dbf05783caa159877f8732ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:28.132916Z","signature_b64":"bzZFwXPP2rwOi/OQaQMjrF7iCEHHiTPUtaQn5hRlPR6jl5vlusbZNvccXM9rjgxHNz3beaXl9NGmrVgpfTIlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a1ae2e3ce8eef48b9e382f32f2c27f2d79a3e1d3321e616750d1a7137c04cf1","last_reissued_at":"2026-05-18T04:33:28.132441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:28.132441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Greg Markowsky, Jack H. Koolen, Jongyook Park","submitted_at":"2010-12-13T05:16:45Z","abstract_excerpt":"In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2/k<=C. This extends a conjecture of Bannai and Ito."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2632","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":"1012.2632","created_at":"2026-05-18T04:33:28.132502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.2632v1","created_at":"2026-05-18T04:33:28.132502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2632","created_at":"2026-05-18T04:33:28.132502+00:00"},{"alias_kind":"pith_short_12","alias_value":"DINOFY6OR3XU","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DINOFY6OR3XUROPD","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DINOFY6O","created_at":"2026-05-18T12:26:06.534383+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/DINOFY6OR3XUROPDQLZS6LBH6L","json":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L.json","graph_json":"https://pith.science/api/pith-number/DINOFY6OR3XUROPDQLZS6LBH6L/graph.json","events_json":"https://pith.science/api/pith-number/DINOFY6OR3XUROPDQLZS6LBH6L/events.json","paper":"https://pith.science/paper/DINOFY6O"},"agent_actions":{"view_html":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L","download_json":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L.json","view_paper":"https://pith.science/paper/DINOFY6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.2632&json=true","fetch_graph":"https://pith.science/api/pith-number/DINOFY6OR3XUROPDQLZS6LBH6L/graph.json","fetch_events":"https://pith.science/api/pith-number/DINOFY6OR3XUROPDQLZS6LBH6L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L/action/storage_attestation","attest_author":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L/action/author_attestation","sign_citation":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L/action/citation_signature","submit_replication":"https://pith.science/pith/DINOFY6OR3XUROPDQLZS6LBH6L/action/replication_record"}},"created_at":"2026-05-18T04:33:28.132502+00:00","updated_at":"2026-05-18T04:33:28.132502+00:00"}