{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BAQW2T3SDSTLKCTTQYNYG5U3PF","short_pith_number":"pith:BAQW2T3S","canonical_record":{"source":{"id":"1212.0722","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-04T13:58:22Z","cross_cats_sorted":[],"title_canon_sha256":"6f3bff122211799b35b989232538121e6e2c99feddcc342046fcc8018c186f7a","abstract_canon_sha256":"633848d3f92ab817cbe5bf572c2eb8d4cf6649e95b3eda3b8e3d8c6da619a6d8"},"schema_version":"1.0"},"canonical_sha256":"08216d4f721ca6b50a73861b83769b797f99e9a42126e4ba0e25cfbd3885224a","source":{"kind":"arxiv","id":"1212.0722","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0722","created_at":"2026-05-18T01:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0722v2","created_at":"2026-05-18T01:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0722","created_at":"2026-05-18T01:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"BAQW2T3SDSTL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BAQW2T3SDSTLKCTT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BAQW2T3S","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BAQW2T3SDSTLKCTTQYNYG5U3PF","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0722","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-04T13:58:22Z","cross_cats_sorted":[],"title_canon_sha256":"6f3bff122211799b35b989232538121e6e2c99feddcc342046fcc8018c186f7a","abstract_canon_sha256":"633848d3f92ab817cbe5bf572c2eb8d4cf6649e95b3eda3b8e3d8c6da619a6d8"},"schema_version":"1.0"},"canonical_sha256":"08216d4f721ca6b50a73861b83769b797f99e9a42126e4ba0e25cfbd3885224a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:47.909737Z","signature_b64":"axZNBh10tyLCsEFKhOMB7W6OcBxkWmBMKjdypd5fsRxdNOTmxJ1Lc7fQswLaqHgmZ3+rEz0ovDuuAJCzyXtMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08216d4f721ca6b50a73861b83769b797f99e9a42126e4ba0e25cfbd3885224a","last_reissued_at":"2026-05-18T01:52:47.909378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:47.909378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0722","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:52:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8oy4CR9PiqvZdWeidurWEPttUQbBR05vB+FDDdIi8OUoIZaQ8v/Jx6ybVXMH4CcCtIqDSJgedDCGbO3C35ejDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:53:58.379107Z"},"content_sha256":"9872c90af0fd386c41c6a3deac228089809f52f6de90328435ff96327cab6bf3","schema_version":"1.0","event_id":"sha256:9872c90af0fd386c41c6a3deac228089809f52f6de90328435ff96327cab6bf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BAQW2T3SDSTLKCTTQYNYG5U3PF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The toroidal block and the genus expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Amir-Kian Kashani-Poor, Jan Troost","submitted_at":"2012-12-04T13:58:22Z","abstract_excerpt":"We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via geometric engineering from the topological string. This point of view uncovers modular properties of the one-point conformal block on a torus with complexified intermediate momenta: in the large intermediate weight limit, it is a power series whose coefficients are quasi-modular forms. The all-genus viewpoint that the conformal field theory approach lends to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0722","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:52:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvMsmDwdtPjKzLOC8023ztToFWj2DAUzWX/k2SqfG0LWIRD4w6gttfqrCEEh0vrIap4V5uK6TI+znPcXXPe1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:53:58.379472Z"},"content_sha256":"34bccdd42ee5b8fe5147754b3e97336a33dae123cb6d7d304bb0b1a80ee6ea69","schema_version":"1.0","event_id":"sha256:34bccdd42ee5b8fe5147754b3e97336a33dae123cb6d7d304bb0b1a80ee6ea69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAQW2T3SDSTLKCTTQYNYG5U3PF/bundle.json","state_url":"https://pith.science/pith/BAQW2T3SDSTLKCTTQYNYG5U3PF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAQW2T3SDSTLKCTTQYNYG5U3PF/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":"2026-06-03T09:53:58Z","links":{"resolver":"https://pith.science/pith/BAQW2T3SDSTLKCTTQYNYG5U3PF","bundle":"https://pith.science/pith/BAQW2T3SDSTLKCTTQYNYG5U3PF/bundle.json","state":"https://pith.science/pith/BAQW2T3SDSTLKCTTQYNYG5U3PF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAQW2T3SDSTLKCTTQYNYG5U3PF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BAQW2T3SDSTLKCTTQYNYG5U3PF","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":"633848d3f92ab817cbe5bf572c2eb8d4cf6649e95b3eda3b8e3d8c6da619a6d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-04T13:58:22Z","title_canon_sha256":"6f3bff122211799b35b989232538121e6e2c99feddcc342046fcc8018c186f7a"},"schema_version":"1.0","source":{"id":"1212.0722","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0722","created_at":"2026-05-18T01:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0722v2","created_at":"2026-05-18T01:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0722","created_at":"2026-05-18T01:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"BAQW2T3SDSTL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BAQW2T3SDSTLKCTT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BAQW2T3S","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:34bccdd42ee5b8fe5147754b3e97336a33dae123cb6d7d304bb0b1a80ee6ea69","target":"graph","created_at":"2026-05-18T01:52:47Z","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 correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via geometric engineering from the topological string. This point of view uncovers modular properties of the one-point conformal block on a torus with complexified intermediate momenta: in the large intermediate weight limit, it is a power series whose coefficients are quasi-modular forms. The all-genus viewpoint that the conformal field theory approach lends to th","authors_text":"Amir-Kian Kashani-Poor, Jan Troost","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-04T13:58:22Z","title":"The toroidal block and the genus expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0722","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":"sha256:9872c90af0fd386c41c6a3deac228089809f52f6de90328435ff96327cab6bf3","target":"record","created_at":"2026-05-18T01:52:47Z","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":"633848d3f92ab817cbe5bf572c2eb8d4cf6649e95b3eda3b8e3d8c6da619a6d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-04T13:58:22Z","title_canon_sha256":"6f3bff122211799b35b989232538121e6e2c99feddcc342046fcc8018c186f7a"},"schema_version":"1.0","source":{"id":"1212.0722","kind":"arxiv","version":2}},"canonical_sha256":"08216d4f721ca6b50a73861b83769b797f99e9a42126e4ba0e25cfbd3885224a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08216d4f721ca6b50a73861b83769b797f99e9a42126e4ba0e25cfbd3885224a","first_computed_at":"2026-05-18T01:52:47.909378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:47.909378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"axZNBh10tyLCsEFKhOMB7W6OcBxkWmBMKjdypd5fsRxdNOTmxJ1Lc7fQswLaqHgmZ3+rEz0ovDuuAJCzyXtMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:47.909737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0722","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9872c90af0fd386c41c6a3deac228089809f52f6de90328435ff96327cab6bf3","sha256:34bccdd42ee5b8fe5147754b3e97336a33dae123cb6d7d304bb0b1a80ee6ea69"],"state_sha256":"5b0f1605cebc4906199a2897d1a86779fa7aa1e3f2e864c6b9d2d56057eb4315"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JiUOVEWfJ9RzxMUlOsGzAzSQ3dVXsivvgnU350DKHlBw1mdGemMS/c+g/IYuIke5u1XT3lrSlxm8fCnTkeq3DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:53:58.381408Z","bundle_sha256":"f3889828d1b5e27987846dcab8da1aff8249eda1b59a351ceb17c5e36b7df38b"}}