{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:EA45Y6GAURGMW5UCCEFYOVAE4B","short_pith_number":"pith:EA45Y6GA","canonical_record":{"source":{"id":"2309.17308","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-09-29T15:05:58Z","cross_cats_sorted":["hep-th","math.AG","math.QA"],"title_canon_sha256":"43bb3ebf012d5c8365abfcbac67c17fc4649acc62a8519c5803d6caa2d09e776","abstract_canon_sha256":"c759ec8176423813c61fa9b4923ecafc2433cff514fdd14be27a1bd2460b6a0e"},"schema_version":"1.0"},"canonical_sha256":"2039dc78c0a44ccb7682110b875404e051e3449424157ee38bf677ff31848096","source":{"kind":"arxiv","id":"2309.17308","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.17308","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"arxiv_version","alias_value":"2309.17308v2","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.17308","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"pith_short_12","alias_value":"EA45Y6GAURGM","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"pith_short_16","alias_value":"EA45Y6GAURGMW5UC","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"pith_short_8","alias_value":"EA45Y6GA","created_at":"2026-07-05T07:20:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:EA45Y6GAURGMW5UCCEFYOVAE4B","target":"record","payload":{"canonical_record":{"source":{"id":"2309.17308","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-09-29T15:05:58Z","cross_cats_sorted":["hep-th","math.AG","math.QA"],"title_canon_sha256":"43bb3ebf012d5c8365abfcbac67c17fc4649acc62a8519c5803d6caa2d09e776","abstract_canon_sha256":"c759ec8176423813c61fa9b4923ecafc2433cff514fdd14be27a1bd2460b6a0e"},"schema_version":"1.0"},"canonical_sha256":"2039dc78c0a44ccb7682110b875404e051e3449424157ee38bf677ff31848096","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:20:54.061486Z","signature_b64":"qpjOsaXkIl76gmO+IZr1ckEkqyKtmEcuM/k9WcMoJrgAJCV5OBf/J6VrLzzTITFLpj3Mwu2aJa9dDkmWnJ5+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2039dc78c0a44ccb7682110b875404e051e3449424157ee38bf677ff31848096","last_reissued_at":"2026-07-05T07:20:54.061085Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:20:54.061085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.17308","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":"2026-07-05T07:20:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"De8HXXP07OVCovtcSCSqBKtfDz2RlrGcHu7PEC//ZQV9rHkB09WkbKoEUcWiaR670jP95TxVUaAESA8MwofEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:34:39.691938Z"},"content_sha256":"f47602cd51199eb0ccbf86a64653d78e2e3b139a7b6804a55bfb74de22e369b0","schema_version":"1.0","event_id":"sha256:f47602cd51199eb0ccbf86a64653d78e2e3b139a7b6804a55bfb74de22e369b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:EA45Y6GAURGMW5UCCEFYOVAE4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with $\\mathcal{N}=4$ Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Sven M\\\"oller, Tomoyuki Arakawa, Toshiro Kuwabara","submitted_at":"2023-09-29T15:05:58Z","abstract_excerpt":"To each complex reflection group $\\Gamma$ one can attach a canonical symplectic singularity $\\mathcal{M}_\\Gamma$ arXiv:math/9903070. Motivated by the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and Rastelli arXiv:1810.03612 conjectured the existence of a supersymmetric vertex operator superalgebra $\\mathsf{W}_\\Gamma$ whose associated variety is isomorphic to $\\mathcal{M}_\\Gamma$. We prove this conjecture when the complex reflection group $\\Gamma$ is the symmetric group $S_N$ by constructing a sheaf of $\\hbar$-adic vertex operator superalgebras on the Hilbert scheme of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.17308","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.17308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:20:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ukXWKk0yhD9TLcGnHKbgaN40T2162kaPw8qmY0ef8AENT6oRg+ndXLGJPhORYX7DGPj/sZSRBtdyOrxWC1RdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:34:39.692866Z"},"content_sha256":"d0969063d91de1597adeece47ea5490465dd6c331034080943c12b3e4fe896fb","schema_version":"1.0","event_id":"sha256:d0969063d91de1597adeece47ea5490465dd6c331034080943c12b3e4fe896fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EA45Y6GAURGMW5UCCEFYOVAE4B/bundle.json","state_url":"https://pith.science/pith/EA45Y6GAURGMW5UCCEFYOVAE4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EA45Y6GAURGMW5UCCEFYOVAE4B/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":"2026-08-09T14:34:39Z","links":{"resolver":"https://pith.science/pith/EA45Y6GAURGMW5UCCEFYOVAE4B","bundle":"https://pith.science/pith/EA45Y6GAURGMW5UCCEFYOVAE4B/bundle.json","state":"https://pith.science/pith/EA45Y6GAURGMW5UCCEFYOVAE4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EA45Y6GAURGMW5UCCEFYOVAE4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:EA45Y6GAURGMW5UCCEFYOVAE4B","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":"c759ec8176423813c61fa9b4923ecafc2433cff514fdd14be27a1bd2460b6a0e","cross_cats_sorted":["hep-th","math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-09-29T15:05:58Z","title_canon_sha256":"43bb3ebf012d5c8365abfcbac67c17fc4649acc62a8519c5803d6caa2d09e776"},"schema_version":"1.0","source":{"id":"2309.17308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.17308","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"arxiv_version","alias_value":"2309.17308v2","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.17308","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"pith_short_12","alias_value":"EA45Y6GAURGM","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"pith_short_16","alias_value":"EA45Y6GAURGMW5UC","created_at":"2026-07-05T07:20:54Z"},{"alias_kind":"pith_short_8","alias_value":"EA45Y6GA","created_at":"2026-07-05T07:20:54Z"}],"graph_snapshots":[{"event_id":"sha256:d0969063d91de1597adeece47ea5490465dd6c331034080943c12b3e4fe896fb","target":"graph","created_at":"2026-07-05T07:20:54Z","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/2309.17308/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"To each complex reflection group $\\Gamma$ one can attach a canonical symplectic singularity $\\mathcal{M}_\\Gamma$ arXiv:math/9903070. Motivated by the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and Rastelli arXiv:1810.03612 conjectured the existence of a supersymmetric vertex operator superalgebra $\\mathsf{W}_\\Gamma$ whose associated variety is isomorphic to $\\mathcal{M}_\\Gamma$. We prove this conjecture when the complex reflection group $\\Gamma$ is the symmetric group $S_N$ by constructing a sheaf of $\\hbar$-adic vertex operator superalgebras on the Hilbert scheme of ","authors_text":"Sven M\\\"oller, Tomoyuki Arakawa, Toshiro Kuwabara","cross_cats":["hep-th","math.AG","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-09-29T15:05:58Z","title":"Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with $\\mathcal{N}=4$ Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.17308","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:f47602cd51199eb0ccbf86a64653d78e2e3b139a7b6804a55bfb74de22e369b0","target":"record","created_at":"2026-07-05T07:20:54Z","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":"c759ec8176423813c61fa9b4923ecafc2433cff514fdd14be27a1bd2460b6a0e","cross_cats_sorted":["hep-th","math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-09-29T15:05:58Z","title_canon_sha256":"43bb3ebf012d5c8365abfcbac67c17fc4649acc62a8519c5803d6caa2d09e776"},"schema_version":"1.0","source":{"id":"2309.17308","kind":"arxiv","version":2}},"canonical_sha256":"2039dc78c0a44ccb7682110b875404e051e3449424157ee38bf677ff31848096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2039dc78c0a44ccb7682110b875404e051e3449424157ee38bf677ff31848096","first_computed_at":"2026-07-05T07:20:54.061085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:20:54.061085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qpjOsaXkIl76gmO+IZr1ckEkqyKtmEcuM/k9WcMoJrgAJCV5OBf/J6VrLzzTITFLpj3Mwu2aJa9dDkmWnJ5+Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:20:54.061486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.17308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f47602cd51199eb0ccbf86a64653d78e2e3b139a7b6804a55bfb74de22e369b0","sha256:d0969063d91de1597adeece47ea5490465dd6c331034080943c12b3e4fe896fb"],"state_sha256":"268740772e2753b8aed94014eba42143ce465e8c2634c50fd4d35cc079bc5c07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxROgBs4aw71+tfG15+yjObfeOQaixBgWas9qKsUyFTdBjaI/KhuOOVsqbM1+3NA3XAWyxa+9odAcfIrwtwpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T14:34:39.701306Z","bundle_sha256":"851a2fab77074c0a1d21daf5deac2d2d4e61ff7602285f3ab08c22cdf9f5f217"}}