{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G2EXLZWFM4TZGWYZ5B2ZE24YS7","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":"072f5ed7eb0fcea6d866118ab9c4cc9217fef7ea5dbdffe6230ae78e11c2271c","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-16T01:58:34Z","title_canon_sha256":"fe80b534fc2d5cc51a399228bbb9362b4170a406d3981841c9c90f86f7cae2ae"},"schema_version":"1.0","source":{"id":"1310.4243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4243","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4243v2","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4243","created_at":"2026-05-18T03:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"G2EXLZWFM4TZ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G2EXLZWFM4TZGWYZ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G2EXLZWF","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:9461af271e76efbf6bb95f84eed52259a25a68b7252bff021e2307c772992ef4","target":"graph","created_at":"2026-05-18T03:02:34Z","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 consider the system $\\mathcal{F}_4(a,b,c)$ of differential equations annihilating Appell's hypergeometric series $F_4(a,b,c;x)$. We find the integral representations for four linearly independent solutions expressed by the hypergeometric series $F_4$. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of $\\mathcal{F}_4(a,b,c)$ and the twisted period relations for the fundamental systems of solutions of $\\mathcal{F}_4$.","authors_text":"Keiji Matsumoto, Yoshiaki Goto","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-16T01:58:34Z","title":"The monodromy representation and twisted period relations for Appell's hypergeometric function F_4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4243","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:fc275d08fe823cc29f3d779d20ca43b13472205bb27d2151742eb4c7c7dac810","target":"record","created_at":"2026-05-18T03:02:34Z","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":"072f5ed7eb0fcea6d866118ab9c4cc9217fef7ea5dbdffe6230ae78e11c2271c","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-16T01:58:34Z","title_canon_sha256":"fe80b534fc2d5cc51a399228bbb9362b4170a406d3981841c9c90f86f7cae2ae"},"schema_version":"1.0","source":{"id":"1310.4243","kind":"arxiv","version":2}},"canonical_sha256":"368975e6c56727935b19e875926b9897e99b4479d6a494f79b92ee17bddb5e87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"368975e6c56727935b19e875926b9897e99b4479d6a494f79b92ee17bddb5e87","first_computed_at":"2026-05-18T03:02:34.253443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:34.253443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3WIez2HoQ3GJ0z5V1q2DhIhxO0FXnmVYa5DGV5CyCskHSPAiJtnLRPzycQUG527Qavm4OYyxneQd7fonDNysCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:34.254279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc275d08fe823cc29f3d779d20ca43b13472205bb27d2151742eb4c7c7dac810","sha256:9461af271e76efbf6bb95f84eed52259a25a68b7252bff021e2307c772992ef4"],"state_sha256":"5a185c628e8ebd9f6d86fef013f20db50a0976d45b697b8bd71b4254ddff40fe"}