{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:G5DDZJDLS775T6NAIGYC7SZTTQ","short_pith_number":"pith:G5DDZJDL","schema_version":"1.0","canonical_sha256":"37463ca46b97ffd9f9a041b02fcb339c013323ac796a2b13d02e27e576b0dbcc","source":{"kind":"arxiv","id":"1203.3257","version":1},"attestation_state":"computed","paper":{"title":"An excess theorem for spherical 2-designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hirotake Kurihara","submitted_at":"2012-03-15T03:24:44Z","abstract_excerpt":"We give an excess theorem for spherical 2-designs. This theorem is a dual version of the spectral excess theorem for graphs, which gives a characterization of distance-regular graphs, among regular graphs in terms of the eigenvalues and the excess. Here we give a characterization of Q-polynomial association schemes among spherical 2-designs."},"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":"1203.3257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-15T03:24:44Z","cross_cats_sorted":[],"title_canon_sha256":"4c1a7a786434ca0f1ad97786a21646ab6f5554b0907cf78ca0189ae780e7e9e3","abstract_canon_sha256":"a67cdea557d89ef3568919d617e36769e4db0e41bbf55f3602fe941cca32eee8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:02.346907Z","signature_b64":"CG3WW37IX3Kll8EJTbZB1AvJhdec72eNSwh9xTxbO3Yh32yXwwRyjKOlxzgvHDNkQ4aTku96LboVP5vA7KBQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37463ca46b97ffd9f9a041b02fcb339c013323ac796a2b13d02e27e576b0dbcc","last_reissued_at":"2026-05-18T04:00:02.346190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:02.346190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An excess theorem for spherical 2-designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hirotake Kurihara","submitted_at":"2012-03-15T03:24:44Z","abstract_excerpt":"We give an excess theorem for spherical 2-designs. This theorem is a dual version of the spectral excess theorem for graphs, which gives a characterization of distance-regular graphs, among regular graphs in terms of the eigenvalues and the excess. Here we give a characterization of Q-polynomial association schemes among spherical 2-designs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3257","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":"1203.3257","created_at":"2026-05-18T04:00:02.346283+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.3257v1","created_at":"2026-05-18T04:00:02.346283+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3257","created_at":"2026-05-18T04:00:02.346283+00:00"},{"alias_kind":"pith_short_12","alias_value":"G5DDZJDLS775","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"G5DDZJDLS775T6NA","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"G5DDZJDL","created_at":"2026-05-18T12:27:06.952714+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/G5DDZJDLS775T6NAIGYC7SZTTQ","json":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ.json","graph_json":"https://pith.science/api/pith-number/G5DDZJDLS775T6NAIGYC7SZTTQ/graph.json","events_json":"https://pith.science/api/pith-number/G5DDZJDLS775T6NAIGYC7SZTTQ/events.json","paper":"https://pith.science/paper/G5DDZJDL"},"agent_actions":{"view_html":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ","download_json":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ.json","view_paper":"https://pith.science/paper/G5DDZJDL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.3257&json=true","fetch_graph":"https://pith.science/api/pith-number/G5DDZJDLS775T6NAIGYC7SZTTQ/graph.json","fetch_events":"https://pith.science/api/pith-number/G5DDZJDLS775T6NAIGYC7SZTTQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ/action/storage_attestation","attest_author":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ/action/author_attestation","sign_citation":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ/action/citation_signature","submit_replication":"https://pith.science/pith/G5DDZJDLS775T6NAIGYC7SZTTQ/action/replication_record"}},"created_at":"2026-05-18T04:00:02.346283+00:00","updated_at":"2026-05-18T04:00:02.346283+00:00"}