{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:NCOOUQMK4LKHI3OTXVDCHISPO2","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":"5c0373eea23fd1affc9e4f5d6de91f64e032967df7c578296a6556edf164b705","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-04-29T18:00:00Z","title_canon_sha256":"0195d7137e2658824ce81455eba20e2a1c3e3a64b41817604714e14c6cbe04e7"},"schema_version":"1.0","source":{"id":"2004.14387","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.14387","created_at":"2026-07-05T01:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"2004.14387v3","created_at":"2026-07-05T01:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.14387","created_at":"2026-07-05T01:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"NCOOUQMK4LKH","created_at":"2026-07-05T01:52:18Z"},{"alias_kind":"pith_short_16","alias_value":"NCOOUQMK4LKHI3OT","created_at":"2026-07-05T01:52:18Z"},{"alias_kind":"pith_short_8","alias_value":"NCOOUQMK","created_at":"2026-07-05T01:52:18Z"}],"graph_snapshots":[{"event_id":"sha256:7fdb29927de52edf9dc0a106ce36ebbe916d3e4b082873841d943b5cd592bbde","target":"graph","created_at":"2026-07-05T01:52:18Z","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/2004.14387/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional $\\mathcal{N} =4$ super Yang-Mills theory on $\\mathbb{CP}^{2}$ for the gauge group $SO(3)$ from the path integral of the effective theory on the Coulomb branch. The holomorphic kernel of this equation, which receives contributions only from the instantons, is not modular but `mock modular'. The partition function has correct modular properties expected from $S$-duality only after including the anomalous nonholomorphic boundary contributions from anti-instantons. Using M-theory duality, w","authors_text":"Atish Dabholkar, Edward Witten, Pavel Putrov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-04-29T18:00:00Z","title":"Duality and Mock Modularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.14387","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":"sha256:0d3231a1f0fe3092d860547990140640841c8a8a6fd1b5ec649b9b9ac7f7d9a3","target":"record","created_at":"2026-07-05T01:52:18Z","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":"5c0373eea23fd1affc9e4f5d6de91f64e032967df7c578296a6556edf164b705","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-04-29T18:00:00Z","title_canon_sha256":"0195d7137e2658824ce81455eba20e2a1c3e3a64b41817604714e14c6cbe04e7"},"schema_version":"1.0","source":{"id":"2004.14387","kind":"arxiv","version":3}},"canonical_sha256":"689cea418ae2d4746dd3bd4623a24f768aa9598d59d6911f38ddffe64807e5f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"689cea418ae2d4746dd3bd4623a24f768aa9598d59d6911f38ddffe64807e5f2","first_computed_at":"2026-07-05T01:52:18.277942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:18.277942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lEIhwIRYpw3G8n3uk8rBi74OeglKjEEISMcKOdNsAb2XB9cxk/yuCoiSpczkdhhW5W/3WoDqRJfp36ZToqlsDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:18.278574Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.14387","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d3231a1f0fe3092d860547990140640841c8a8a6fd1b5ec649b9b9ac7f7d9a3","sha256:7fdb29927de52edf9dc0a106ce36ebbe916d3e4b082873841d943b5cd592bbde"],"state_sha256":"a9037c96cd0d13b098cb5a9a8fc7c5e937aa0194d9cf509d3b1947fa1768a9ae"}