{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XX6W625R56IMJWRBNPVRZEO6BR","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":"613dc259281c75cdd3f2a24dfedb243c07e866c77afa520947a3144dfbf0a693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-03T22:41:18Z","title_canon_sha256":"de49e45bd0d8ed1713c882b9c8486c4171cd74bae6ab6b208d422f8c2688e0e1"},"schema_version":"1.0","source":{"id":"1912.01726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.01726","created_at":"2026-07-05T00:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1912.01726v2","created_at":"2026-07-05T00:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.01726","created_at":"2026-07-05T00:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"XX6W625R56IM","created_at":"2026-07-05T00:43:43Z"},{"alias_kind":"pith_short_16","alias_value":"XX6W625R56IMJWRB","created_at":"2026-07-05T00:43:43Z"},{"alias_kind":"pith_short_8","alias_value":"XX6W625R","created_at":"2026-07-05T00:43:43Z"}],"graph_snapshots":[{"event_id":"sha256:3ab4de712d3f1c5115ba8d9531e429983deac3cd6025acb2800e48b2d3be6766","target":"graph","created_at":"2026-07-05T00:43:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.01726/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Basing on the systems of linear partial differential equations derived from Mellin-Barnes representations and Miller's transformation, we obtain GKZ-hypergeometric systems of one-loop self energy, one-loop triangle, two-loop vacuum, and two-loop sunset diagrams, respectively. The codimension of derived GKZ-hypergeometric system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. Taking GKZ-hypergeometric systems of one-loop self energy, massless one-loop triangle, and two-loop vacuum diagrams as examples, we present in detail how ","authors_text":"Chao-Hsi Chang, Hai-Bin Zhang, Jian-Bin Chen, Tai-Fu Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-03T22:41:18Z","title":"GKZ-hypergeometric systems for Feynman integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01726","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":"sha256:5539c5dbc58e2380abebaebf3b0a83e7a2418c66eb8909ab888626e0cb68c8cd","target":"record","created_at":"2026-07-05T00:43:43Z","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":"613dc259281c75cdd3f2a24dfedb243c07e866c77afa520947a3144dfbf0a693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-03T22:41:18Z","title_canon_sha256":"de49e45bd0d8ed1713c882b9c8486c4171cd74bae6ab6b208d422f8c2688e0e1"},"schema_version":"1.0","source":{"id":"1912.01726","kind":"arxiv","version":2}},"canonical_sha256":"bdfd6f6bb1ef90c4da216beb1c91de0c571639fd755346642246472d0613bbfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdfd6f6bb1ef90c4da216beb1c91de0c571639fd755346642246472d0613bbfd","first_computed_at":"2026-07-05T00:43:43.177708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:43:43.177708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jdj+6aDK5j61y63KNwrUVuwt4hEYLfs5ubtqzJUqPFU/s4zsybbdwoslmT53trySmdqqvBro+5JNsQ/NVVCJAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:43:43.178208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.01726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5539c5dbc58e2380abebaebf3b0a83e7a2418c66eb8909ab888626e0cb68c8cd","sha256:3ab4de712d3f1c5115ba8d9531e429983deac3cd6025acb2800e48b2d3be6766"],"state_sha256":"d81fd3300b03855e4b8f5cf7749461115ce64af62ebfa8c18d7162b863b51f76"}