{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:PSVXI2Y5K3ZL4MS2U6E5SU43HS","short_pith_number":"pith:PSVXI2Y5","schema_version":"1.0","canonical_sha256":"7cab746b1d56f2be325aa789d9539b3cbf2af2b20eccea0251c4a1d66ea63d5d","source":{"kind":"arxiv","id":"0712.4253","version":2},"attestation_state":"computed","paper":{"title":"Determinants of elliptic hypergeometric integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E.M. Rains, V.P. Spiridonov","submitted_at":"2007-12-27T19:37:41Z","abstract_excerpt":"We start from an interpretation of the $BC_2$-symmetric \"Type I\" (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation, and give an extension to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding elliptic beta integral and transformation formula in a new way, by proving both sides satisfy the same difference equations, and that the difference equations satisfy a Galois-theoretical condition that ensures uniqueness of simultaneous solution."},"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":"0712.4253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2007-12-27T19:37:41Z","cross_cats_sorted":[],"title_canon_sha256":"7b8dba93d25edb3481e1629e217e483d8a55dab8c16598a468b89baa7bc2ebe9","abstract_canon_sha256":"2ef4c1b5f62646777d95a01bd4c9325e1c059bb0748cea8e2505bcaa56c8a103"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:55.919627Z","signature_b64":"3n5HEYVl0XlGD3yttPDxDV6iIV56Ld4jaEdkzInN8ONTgrDDETow+yrEhJbgkZK9b8FHPXOGXy6F+BQODgPcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cab746b1d56f2be325aa789d9539b3cbf2af2b20eccea0251c4a1d66ea63d5d","last_reissued_at":"2026-05-18T04:28:55.919206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:55.919206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determinants of elliptic hypergeometric integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E.M. Rains, V.P. Spiridonov","submitted_at":"2007-12-27T19:37:41Z","abstract_excerpt":"We start from an interpretation of the $BC_2$-symmetric \"Type I\" (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation, and give an extension to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding elliptic beta integral and transformation formula in a new way, by proving both sides satisfy the same difference equations, and that the difference equations satisfy a Galois-theoretical condition that ensures uniqueness of simultaneous solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4253","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":"0712.4253","created_at":"2026-05-18T04:28:55.919265+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.4253v2","created_at":"2026-05-18T04:28:55.919265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4253","created_at":"2026-05-18T04:28:55.919265+00:00"},{"alias_kind":"pith_short_12","alias_value":"PSVXI2Y5K3ZL","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"PSVXI2Y5K3ZL4MS2","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"PSVXI2Y5","created_at":"2026-05-18T12:25:55.427421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01530","citing_title":"On Complex Gamma-Function Integrals","ref_index":47,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS","json":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS.json","graph_json":"https://pith.science/api/pith-number/PSVXI2Y5K3ZL4MS2U6E5SU43HS/graph.json","events_json":"https://pith.science/api/pith-number/PSVXI2Y5K3ZL4MS2U6E5SU43HS/events.json","paper":"https://pith.science/paper/PSVXI2Y5"},"agent_actions":{"view_html":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS","download_json":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS.json","view_paper":"https://pith.science/paper/PSVXI2Y5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.4253&json=true","fetch_graph":"https://pith.science/api/pith-number/PSVXI2Y5K3ZL4MS2U6E5SU43HS/graph.json","fetch_events":"https://pith.science/api/pith-number/PSVXI2Y5K3ZL4MS2U6E5SU43HS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS/action/storage_attestation","attest_author":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS/action/author_attestation","sign_citation":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS/action/citation_signature","submit_replication":"https://pith.science/pith/PSVXI2Y5K3ZL4MS2U6E5SU43HS/action/replication_record"}},"created_at":"2026-05-18T04:28:55.919265+00:00","updated_at":"2026-05-18T04:28:55.919265+00:00"}