{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:PSVXI2Y5K3ZL4MS2U6E5SU43HS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2ef4c1b5f62646777d95a01bd4c9325e1c059bb0748cea8e2505bcaa56c8a103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2007-12-27T19:37:41Z","title_canon_sha256":"7b8dba93d25edb3481e1629e217e483d8a55dab8c16598a468b89baa7bc2ebe9"},"schema_version":"1.0","source":{"id":"0712.4253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4253","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4253v2","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4253","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"PSVXI2Y5K3ZL","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"PSVXI2Y5K3ZL4MS2","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"PSVXI2Y5","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:2a535ab91071c6a0df54ed51b10dd0ceebe9a47a7183d2ff4f56e0fb406f70f0","target":"graph","created_at":"2026-05-18T04:28:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"E.M. Rains, V.P. Spiridonov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2007-12-27T19:37:41Z","title":"Determinants of elliptic hypergeometric integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4253","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0e4a61c3d8a6b4bd3888409ffef3f6502dffbc8990a0409d3923c4f295d25944","target":"record","created_at":"2026-05-18T04:28:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2ef4c1b5f62646777d95a01bd4c9325e1c059bb0748cea8e2505bcaa56c8a103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2007-12-27T19:37:41Z","title_canon_sha256":"7b8dba93d25edb3481e1629e217e483d8a55dab8c16598a468b89baa7bc2ebe9"},"schema_version":"1.0","source":{"id":"0712.4253","kind":"arxiv","version":2}},"canonical_sha256":"7cab746b1d56f2be325aa789d9539b3cbf2af2b20eccea0251c4a1d66ea63d5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cab746b1d56f2be325aa789d9539b3cbf2af2b20eccea0251c4a1d66ea63d5d","first_computed_at":"2026-05-18T04:28:55.919206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:55.919206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3n5HEYVl0XlGD3yttPDxDV6iIV56Ld4jaEdkzInN8ONTgrDDETow+yrEhJbgkZK9b8FHPXOGXy6F+BQODgPcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:55.919627Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e4a61c3d8a6b4bd3888409ffef3f6502dffbc8990a0409d3923c4f295d25944","sha256:2a535ab91071c6a0df54ed51b10dd0ceebe9a47a7183d2ff4f56e0fb406f70f0"],"state_sha256":"ec26d789b5a9da970106f6729a512edd559e8184787e555553ddcc1d5ee84afa"}