{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JA27MRT5RAPVIYIRCUCFGA47WZ","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":"f6fae4b23e5e52b14f50530e6644eee812b6b743d25b243e3dc319cef3c8d8e7","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-03-14T17:40:25Z","title_canon_sha256":"32454df7e3280ebe8d1260fd6c977c954624c3f8901ef14b8206c2847ad9d158"},"schema_version":"1.0","source":{"id":"1703.04614","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04614","created_at":"2026-05-18T00:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04614v2","created_at":"2026-05-18T00:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04614","created_at":"2026-05-18T00:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"JA27MRT5RAPV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JA27MRT5RAPVIYIR","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JA27MRT5","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:c674fbc064454ef3ccc796f7c04ef151ee8213b5c838b737da752c6c55ef951e","target":"graph","created_at":"2026-05-18T00:26:00Z","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 4d supersymmetric (special) unitary $\\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of vertex operators and screening charges of the modular double version of elliptic $W_{q,t;q'}(\\Gamma)$ algebras. We also consider a generating function of BPS surface defects supported on $T^2$ and show that it can be identified with a particular coherent state in the Fock module over the elliptic Heisenberg algebra.","authors_text":"Fabrizio Nieri, Maxim Zabzine, Rebecca Lodin","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-03-14T17:40:25Z","title":"Elliptic modular double and 4d partition functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04614","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:d0337a35dbdc37a6d1f58a131d7c557fa2652388b7fe63b8769e954c2231d0d2","target":"record","created_at":"2026-05-18T00:26:00Z","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":"f6fae4b23e5e52b14f50530e6644eee812b6b743d25b243e3dc319cef3c8d8e7","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-03-14T17:40:25Z","title_canon_sha256":"32454df7e3280ebe8d1260fd6c977c954624c3f8901ef14b8206c2847ad9d158"},"schema_version":"1.0","source":{"id":"1703.04614","kind":"arxiv","version":2}},"canonical_sha256":"4835f6467d881f546111150453039fb672234c4a05004315624783b0a475c002","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4835f6467d881f546111150453039fb672234c4a05004315624783b0a475c002","first_computed_at":"2026-05-18T00:26:00.712031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:00.712031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M93qJ4blM/waq25X1nocoTnVNfpYPa5rhC0vTvqyDlmr/05ew6x+5zYKlavEnRviF1hTruAU7VkWfl/e907TDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:00.712745Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04614","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0337a35dbdc37a6d1f58a131d7c557fa2652388b7fe63b8769e954c2231d0d2","sha256:c674fbc064454ef3ccc796f7c04ef151ee8213b5c838b737da752c6c55ef951e"],"state_sha256":"4a426786849d78f8f239764b128608236f865d4f1837f8812770031404c110d7"}