{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GB2CNMFGDIS7EPDJDZ2ZNTND2R","short_pith_number":"pith:GB2CNMFG","canonical_record":{"source":{"id":"1312.6382","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-22T13:33:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"446666dcfb82e048fd3104767b014d8640aad6eee90844c6f4f12e3b7216beae","abstract_canon_sha256":"b0d3407cbfa4191eda503e3858aea7a147d0b5a3c433ede618bd15667c1ca73c"},"schema_version":"1.0"},"canonical_sha256":"307426b0a61a25f23c691e7596cda3d443d138bcf73164e5a58137c29a060369","source":{"kind":"arxiv","id":"1312.6382","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6382","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6382v3","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6382","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"GB2CNMFGDIS7","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GB2CNMFGDIS7EPDJ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GB2CNMFG","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GB2CNMFGDIS7EPDJDZ2ZNTND2R","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6382","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-22T13:33:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"446666dcfb82e048fd3104767b014d8640aad6eee90844c6f4f12e3b7216beae","abstract_canon_sha256":"b0d3407cbfa4191eda503e3858aea7a147d0b5a3c433ede618bd15667c1ca73c"},"schema_version":"1.0"},"canonical_sha256":"307426b0a61a25f23c691e7596cda3d443d138bcf73164e5a58137c29a060369","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:03.929754Z","signature_b64":"Lb9q3yDplS4F0RIH/o10FwtBw0mJZWpgxJqzvzHU2VI4tZXgBbz8Hd8tbFqIDYW04LbADKyrVmZ2muZq62YuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"307426b0a61a25f23c691e7596cda3d443d138bcf73164e5a58137c29a060369","last_reissued_at":"2026-05-18T01:20:03.929278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:03.929278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6382","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSJvqq1eyfADw93K/oBDzg4Jwr9ZnNCKVmDz1Mxfh1Dr8yMU3cFzAuPS4YOqilOxsYMYf3Fs5gOmD8zC7oEpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:52:46.386383Z"},"content_sha256":"48747fc20e55ad036abc36bd6f997d009f5c343e47dae8381cbdad518929e37f","schema_version":"1.0","event_id":"sha256:48747fc20e55ad036abc36bd6f997d009f5c343e47dae8381cbdad518929e37f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GB2CNMFGDIS7EPDJDZ2ZNTND2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. Marshakov, P. Gavrylenko","submitted_at":"2013-12-22T13:33:03Z","abstract_excerpt":"We study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and bare couplings. The residue formulas for the third derivatives of extended prepotentials are proven, which lead to effective way of their computation, as expansion in the weak-coupling regime. We discuss also the differential equations, following from the residue formulas, including the WDVV equations, proven to be valid for the $SU(2)$ quiver gauge theories. As a particular example we consider the constrained conforma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6382","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8uwpyfVsZnWOub9wdA4w5xz7OUntCKfer+kgV7jKN5z72+5JlQ6xmCH+xY9lKNBMrLIkdUEyNOWfh6MedCnZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:52:46.386739Z"},"content_sha256":"96bb04c4245a342c82409107bbbc477c37b0633cf9ee5b3d1db2564a382a3f82","schema_version":"1.0","event_id":"sha256:96bb04c4245a342c82409107bbbc477c37b0633cf9ee5b3d1db2564a382a3f82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GB2CNMFGDIS7EPDJDZ2ZNTND2R/bundle.json","state_url":"https://pith.science/pith/GB2CNMFGDIS7EPDJDZ2ZNTND2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GB2CNMFGDIS7EPDJDZ2ZNTND2R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T09:52:46Z","links":{"resolver":"https://pith.science/pith/GB2CNMFGDIS7EPDJDZ2ZNTND2R","bundle":"https://pith.science/pith/GB2CNMFGDIS7EPDJDZ2ZNTND2R/bundle.json","state":"https://pith.science/pith/GB2CNMFGDIS7EPDJDZ2ZNTND2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GB2CNMFGDIS7EPDJDZ2ZNTND2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GB2CNMFGDIS7EPDJDZ2ZNTND2R","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":"b0d3407cbfa4191eda503e3858aea7a147d0b5a3c433ede618bd15667c1ca73c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-22T13:33:03Z","title_canon_sha256":"446666dcfb82e048fd3104767b014d8640aad6eee90844c6f4f12e3b7216beae"},"schema_version":"1.0","source":{"id":"1312.6382","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6382","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6382v3","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6382","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"GB2CNMFGDIS7","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GB2CNMFGDIS7EPDJ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GB2CNMFG","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:96bb04c4245a342c82409107bbbc477c37b0633cf9ee5b3d1db2564a382a3f82","target":"graph","created_at":"2026-05-18T01:20:03Z","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 study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and bare couplings. The residue formulas for the third derivatives of extended prepotentials are proven, which lead to effective way of their computation, as expansion in the weak-coupling regime. We discuss also the differential equations, following from the residue formulas, including the WDVV equations, proven to be valid for the $SU(2)$ quiver gauge theories. As a particular example we consider the constrained conforma","authors_text":"A. Marshakov, P. Gavrylenko","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-22T13:33:03Z","title":"Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6382","kind":"arxiv","version":3},"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":"sha256:48747fc20e55ad036abc36bd6f997d009f5c343e47dae8381cbdad518929e37f","target":"record","created_at":"2026-05-18T01:20:03Z","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":"b0d3407cbfa4191eda503e3858aea7a147d0b5a3c433ede618bd15667c1ca73c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-22T13:33:03Z","title_canon_sha256":"446666dcfb82e048fd3104767b014d8640aad6eee90844c6f4f12e3b7216beae"},"schema_version":"1.0","source":{"id":"1312.6382","kind":"arxiv","version":3}},"canonical_sha256":"307426b0a61a25f23c691e7596cda3d443d138bcf73164e5a58137c29a060369","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"307426b0a61a25f23c691e7596cda3d443d138bcf73164e5a58137c29a060369","first_computed_at":"2026-05-18T01:20:03.929278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:03.929278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lb9q3yDplS4F0RIH/o10FwtBw0mJZWpgxJqzvzHU2VI4tZXgBbz8Hd8tbFqIDYW04LbADKyrVmZ2muZq62YuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:03.929754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6382","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48747fc20e55ad036abc36bd6f997d009f5c343e47dae8381cbdad518929e37f","sha256:96bb04c4245a342c82409107bbbc477c37b0633cf9ee5b3d1db2564a382a3f82"],"state_sha256":"efb10b8bdfe9bcb27ac432fe87690494129d5b407ba48ef85ae84850552298dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"on1uJWGS1f1b+f2JmFkRBqe4Odwd/UaZaC4sV5FM38Ybr8QSmoBBblEIJQzn01LWhbPzFkfRmR6ptd2eMTZaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:52:46.388693Z","bundle_sha256":"d5e2df7146b217231377382fd5286ef960a80ef583b7747ad1c6dba692a16b09"}}