{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CA3C6G6QC3MN3PZRWP6ANNYSA2","short_pith_number":"pith:CA3C6G6Q","schema_version":"1.0","canonical_sha256":"10362f1bd016d8ddbf31b3fc06b712069b20652c60664ef1e3a0c14d7899a301","source":{"kind":"arxiv","id":"1604.00480","version":2},"attestation_state":"computed","paper":{"title":"Three-Term Relations for 3F2(1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Akihito Ebisu, Katsunori Iwasaki","submitted_at":"2016-04-02T09:27:22Z","abstract_excerpt":"For the hypergeometric function of unit argument 3F2(1) we prove the existence and uniqueness of three-term relations with arbitrary integer shifts. We show that not only the original 3F2(1) function but also other five functions related to it satisfy one and the same three-term relation. This fact is referred to as simultaneousness. The uniqueness and simultaneousness provide three-term relations with a group symmetry of order 72."},"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":"1604.00480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-02T09:27:22Z","cross_cats_sorted":[],"title_canon_sha256":"0c9e7388877ba3fce1af24bd7abf71872e2dd327436862eaaa40f2a619805d4d","abstract_canon_sha256":"f1010b82ac50ed18d9c3fd5e076a6a4177cc745656a101edeb16e3d9fecbaa99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:09.863163Z","signature_b64":"7eIFMXKpkdFPiXyOAQeeQlSyhB61sgtVA90J5Pr0mVv5NLEMyekUvYmp6Bd/UfufF9qcRckTxoYhdjLruQrvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10362f1bd016d8ddbf31b3fc06b712069b20652c60664ef1e3a0c14d7899a301","last_reissued_at":"2026-05-18T00:36:09.862563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:09.862563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-Term Relations for 3F2(1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Akihito Ebisu, Katsunori Iwasaki","submitted_at":"2016-04-02T09:27:22Z","abstract_excerpt":"For the hypergeometric function of unit argument 3F2(1) we prove the existence and uniqueness of three-term relations with arbitrary integer shifts. We show that not only the original 3F2(1) function but also other five functions related to it satisfy one and the same three-term relation. This fact is referred to as simultaneousness. The uniqueness and simultaneousness provide three-term relations with a group symmetry of order 72."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00480","kind":"arxiv","version":2},"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":"1604.00480","created_at":"2026-05-18T00:36:09.862670+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.00480v2","created_at":"2026-05-18T00:36:09.862670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00480","created_at":"2026-05-18T00:36:09.862670+00:00"},{"alias_kind":"pith_short_12","alias_value":"CA3C6G6QC3MN","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CA3C6G6QC3MN3PZR","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CA3C6G6Q","created_at":"2026-05-18T12:30:09.641336+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/CA3C6G6QC3MN3PZRWP6ANNYSA2","json":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2.json","graph_json":"https://pith.science/api/pith-number/CA3C6G6QC3MN3PZRWP6ANNYSA2/graph.json","events_json":"https://pith.science/api/pith-number/CA3C6G6QC3MN3PZRWP6ANNYSA2/events.json","paper":"https://pith.science/paper/CA3C6G6Q"},"agent_actions":{"view_html":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2","download_json":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2.json","view_paper":"https://pith.science/paper/CA3C6G6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.00480&json=true","fetch_graph":"https://pith.science/api/pith-number/CA3C6G6QC3MN3PZRWP6ANNYSA2/graph.json","fetch_events":"https://pith.science/api/pith-number/CA3C6G6QC3MN3PZRWP6ANNYSA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2/action/storage_attestation","attest_author":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2/action/author_attestation","sign_citation":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2/action/citation_signature","submit_replication":"https://pith.science/pith/CA3C6G6QC3MN3PZRWP6ANNYSA2/action/replication_record"}},"created_at":"2026-05-18T00:36:09.862670+00:00","updated_at":"2026-05-18T00:36:09.862670+00:00"}