{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:WL7PU2S76GKNCHJG77ZAHAZUWH","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":"2ddc2b2468e246e89ab4e9815cc6ad6cb72d75ce7c3563f1b199761cef248023","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-03-08T15:40:51Z","title_canon_sha256":"c1b91f45351b01e926361a1919993d956a094f1ca093a9ca0b689c28bbc0f28f"},"schema_version":"1.0","source":{"id":"2003.03802","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.03802","created_at":"2026-07-05T07:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"2003.03802v4","created_at":"2026-07-05T07:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.03802","created_at":"2026-07-05T07:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"WL7PU2S76GKN","created_at":"2026-07-05T07:38:22Z"},{"alias_kind":"pith_short_16","alias_value":"WL7PU2S76GKNCHJG","created_at":"2026-07-05T07:38:22Z"},{"alias_kind":"pith_short_8","alias_value":"WL7PU2S7","created_at":"2026-07-05T07:38:22Z"}],"graph_snapshots":[{"event_id":"sha256:02427267f562486019f61f4c28a318768476e82d1d4caea6bd1f4f1ee4d6c07e","target":"graph","created_at":"2026-07-05T07:38:22Z","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/2003.03802/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Virasoro conformal blocks are a family of important functions defined as power series via the Virasoro algebra. They are a fundamental input to the conformal bootstrap program for 2D conformal field theory (CFT) and are closely related to four dimensional supersymmetric gauge theory through the Alday-Gaiotto-Tachikawa correspondence. The present work provides a probabilistic construction of the 1-point toric Virasoro conformal block for central change greater than 25. More precisely, we construct an analytic function using a probabilistic tool called Gaussian multiplicative chaos (GMC) and pro","authors_text":"Guillaume Remy, Promit Ghosal, Xin Sun, Yi Sun","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-03-08T15:40:51Z","title":"Probabilistic conformal blocks for Liouville CFT on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.03802","kind":"arxiv","version":4},"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:b65ec593582192aefbcc177301dfa557bc593e33c1ea65cdfcd259540e5d9396","target":"record","created_at":"2026-07-05T07:38:22Z","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":"2ddc2b2468e246e89ab4e9815cc6ad6cb72d75ce7c3563f1b199761cef248023","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-03-08T15:40:51Z","title_canon_sha256":"c1b91f45351b01e926361a1919993d956a094f1ca093a9ca0b689c28bbc0f28f"},"schema_version":"1.0","source":{"id":"2003.03802","kind":"arxiv","version":4}},"canonical_sha256":"b2fefa6a5ff194d11d26fff2038334b1ee3c1dd7bc72b7526085b8a72ab12012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2fefa6a5ff194d11d26fff2038334b1ee3c1dd7bc72b7526085b8a72ab12012","first_computed_at":"2026-07-05T07:38:22.674120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:38:22.674120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+gNNB0eie5PcJmXtNP8sDOFwMNn92Ax/gSvsJ2hjZUINHQ5gmXhdIhA/ZhAcshRDzUKKsHcA4bz+y6hvpsPDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:38:22.674605Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.03802","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b65ec593582192aefbcc177301dfa557bc593e33c1ea65cdfcd259540e5d9396","sha256:02427267f562486019f61f4c28a318768476e82d1d4caea6bd1f4f1ee4d6c07e"],"state_sha256":"a6f0689f1aca894923ecf9a246de2bbc773b704be7945d537f9a573118415909"}