{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BS3MYFRQN5UQG5NBMMRAYHB2HH","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":"55e1f900395e7103f57be17386a52cd233e937c04ef145e6a2bb603bb354fa2e","cross_cats_sorted":["math.AG","math.DG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-09-09T14:27:15Z","title_canon_sha256":"58aad8360eaf479d431fb792ce11cecc9c1d587a55f184fe2d5b23b6a5076f2e"},"schema_version":"1.0","source":{"id":"2109.04302","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.04302","created_at":"2026-07-05T04:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"2109.04302v2","created_at":"2026-07-05T04:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.04302","created_at":"2026-07-05T04:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"BS3MYFRQN5UQ","created_at":"2026-07-05T04:12:02Z"},{"alias_kind":"pith_short_16","alias_value":"BS3MYFRQN5UQG5NB","created_at":"2026-07-05T04:12:02Z"},{"alias_kind":"pith_short_8","alias_value":"BS3MYFRQ","created_at":"2026-07-05T04:12:02Z"}],"graph_snapshots":[{"event_id":"sha256:113a3f9ea16d4c060f0af1076ce28af894a9a9964479b86604a638325118fcc2","target":"graph","created_at":"2026-07-05T04:12:02Z","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/2109.04302/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit the low-energy effective $U(1)$ action of topologically twisted $\\mathcal N=2$ SYM theory with gauge group of rank one on a generic oriented smooth 4-manifold $X$ with nontrivial fundamental group. After including a specific new set of $\\mathcal Q$-exact operators to the known action, we express the integrand of the path integral of the low-energy $U(1)$ theory as an anti-holomorphic derivative. This allows us to use the theory of mock modular forms and indefinite theta functions for the explicit evaluation of correlation functions of the theory, including but not restricted to thos","authors_text":"Elias Furrer, Georgios Korpas, Johannes Aspman, Meng-Chwan Tan, Zhi-Cong Ong","cross_cats":["math.AG","math.DG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-09-09T14:27:15Z","title":"The $u$-plane integral, mock modularity and enumerative geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.04302","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":"sha256:42daebfab7f80811ef928644af33c308fdfaa8b73c718129242d3515aba96966","target":"record","created_at":"2026-07-05T04:12:02Z","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":"55e1f900395e7103f57be17386a52cd233e937c04ef145e6a2bb603bb354fa2e","cross_cats_sorted":["math.AG","math.DG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-09-09T14:27:15Z","title_canon_sha256":"58aad8360eaf479d431fb792ce11cecc9c1d587a55f184fe2d5b23b6a5076f2e"},"schema_version":"1.0","source":{"id":"2109.04302","kind":"arxiv","version":2}},"canonical_sha256":"0cb6cc16306f690375a163220c1c3a39d918d31d8c21b92298aa0ced2c7a35fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cb6cc16306f690375a163220c1c3a39d918d31d8c21b92298aa0ced2c7a35fd","first_computed_at":"2026-07-05T04:12:02.440632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:12:02.440632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CKYqIZ5GojRD6zLtd5S+/y3nIeyMReZ1LQvu8lC+Cva+4LLigC2Jzu77uSvrMlVv/ND9ue5k+Ypkk57w1IkYCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:12:02.441122Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.04302","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42daebfab7f80811ef928644af33c308fdfaa8b73c718129242d3515aba96966","sha256:113a3f9ea16d4c060f0af1076ce28af894a9a9964479b86604a638325118fcc2"],"state_sha256":"c64d6cc2f722dbce9d8ef5db3531faec6b9b69629297912e926e7064962ff0e9"}