{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:KCDZANWUUHZPJ5ID2VD3ECNBG6","short_pith_number":"pith:KCDZANWU","canonical_record":{"source":{"id":"2312.13900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-21T14:46:03Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"5c23645b4c27cee4fd63ed4038eece55cff9e0f7a3888c2ee679093992c1c457","abstract_canon_sha256":"2dc2dc69b6b993dc6861e66524447fa1de55081bc003746c91114bbb8e060c42"},"schema_version":"1.0"},"canonical_sha256":"50879036d4a1f2f4f503d547b209a137abd37296c5c24e2f5772276001b3efd2","source":{"kind":"arxiv","id":"2312.13900","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.13900","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"arxiv_version","alias_value":"2312.13900v2","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13900","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"pith_short_12","alias_value":"KCDZANWUUHZP","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"pith_short_16","alias_value":"KCDZANWUUHZPJ5ID","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"pith_short_8","alias_value":"KCDZANWU","created_at":"2026-05-20T14:03:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:KCDZANWUUHZPJ5ID2VD3ECNBG6","target":"record","payload":{"canonical_record":{"source":{"id":"2312.13900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-21T14:46:03Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"5c23645b4c27cee4fd63ed4038eece55cff9e0f7a3888c2ee679093992c1c457","abstract_canon_sha256":"2dc2dc69b6b993dc6861e66524447fa1de55081bc003746c91114bbb8e060c42"},"schema_version":"1.0"},"canonical_sha256":"50879036d4a1f2f4f503d547b209a137abd37296c5c24e2f5772276001b3efd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T14:03:17.071231Z","signature_b64":"6/KW0xxwvyygQdNxofYf950YyIBrKauuuMlRaESacChZY1GFIVQHRnpCoKGuToELuI60TgBCOr/SkX48SSZGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50879036d4a1f2f4f503d547b209a137abd37296c5c24e2f5772276001b3efd2","last_reissued_at":"2026-05-20T14:03:17.070752Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T14:03:17.070752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.13900","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":"2026-05-20T14:03:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IXaW2rp+Bpi2n4rrem8YNPNxu0mUWY3ZUUUv2kwBWdDsrSfaN4qx/xlDDBVCMdlU6X45k65gOCWvZ7f2NANYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:27:58.293365Z"},"content_sha256":"803e3fe84fe59147d4ee89275f3a7026e2aaea729d0b0a60ab72d5f98890a631","schema_version":"1.0","event_id":"sha256:803e3fe84fe59147d4ee89275f3a7026e2aaea729d0b0a60ab72d5f98890a631"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:KCDZANWUUHZPJ5ID2VD3ECNBG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher equations of motion at level 2 in Liouville CFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.PR","authors_text":"Baojun Wu, Guillaume Baverez","submitted_at":"2023-12-21T14:46:03Z","abstract_excerpt":"We prove conjectures of Zamolodchikov and Belavin-Belavin in Liouville conformal field theory (CFT), which are generalisations of the celebrated Belavin-Polyakov-Zamolodchikov equations known as the higher equations of motion. Algebraically, these equations give examples of non-zero singular states in Virasoro modules, which is a relatively rare phenomenon in the physical study of CFT. In probability theory, these equations and their variants have been instrumental in the rigorous derivation of the structure constants of Liouville CFT in the unit disc. The proof builds on a previous work of ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13900","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/2312.13900/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":"2026-05-20T14:03:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ueMOTFylM3Ko4ZPBWClVqSIzzGLQa5W6iVUwJESElES7ZDgUqSZ3efOUsqeYn2lMqLholtglOxKehcAqI3dXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:27:58.294050Z"},"content_sha256":"ad62c403361394c98567e2f5a59ba5162be34080994e92a31e063f060db33fff","schema_version":"1.0","event_id":"sha256:ad62c403361394c98567e2f5a59ba5162be34080994e92a31e063f060db33fff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCDZANWUUHZPJ5ID2VD3ECNBG6/bundle.json","state_url":"https://pith.science/pith/KCDZANWUUHZPJ5ID2VD3ECNBG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCDZANWUUHZPJ5ID2VD3ECNBG6/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":"2026-05-25T23:27:58Z","links":{"resolver":"https://pith.science/pith/KCDZANWUUHZPJ5ID2VD3ECNBG6","bundle":"https://pith.science/pith/KCDZANWUUHZPJ5ID2VD3ECNBG6/bundle.json","state":"https://pith.science/pith/KCDZANWUUHZPJ5ID2VD3ECNBG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCDZANWUUHZPJ5ID2VD3ECNBG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KCDZANWUUHZPJ5ID2VD3ECNBG6","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":"2dc2dc69b6b993dc6861e66524447fa1de55081bc003746c91114bbb8e060c42","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-21T14:46:03Z","title_canon_sha256":"5c23645b4c27cee4fd63ed4038eece55cff9e0f7a3888c2ee679093992c1c457"},"schema_version":"1.0","source":{"id":"2312.13900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.13900","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"arxiv_version","alias_value":"2312.13900v2","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13900","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"pith_short_12","alias_value":"KCDZANWUUHZP","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"pith_short_16","alias_value":"KCDZANWUUHZPJ5ID","created_at":"2026-05-20T14:03:17Z"},{"alias_kind":"pith_short_8","alias_value":"KCDZANWU","created_at":"2026-05-20T14:03:17Z"}],"graph_snapshots":[{"event_id":"sha256:ad62c403361394c98567e2f5a59ba5162be34080994e92a31e063f060db33fff","target":"graph","created_at":"2026-05-20T14:03:17Z","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/2312.13900/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove conjectures of Zamolodchikov and Belavin-Belavin in Liouville conformal field theory (CFT), which are generalisations of the celebrated Belavin-Polyakov-Zamolodchikov equations known as the higher equations of motion. Algebraically, these equations give examples of non-zero singular states in Virasoro modules, which is a relatively rare phenomenon in the physical study of CFT. In probability theory, these equations and their variants have been instrumental in the rigorous derivation of the structure constants of Liouville CFT in the unit disc. The proof builds on a previous work of ou","authors_text":"Baojun Wu, Guillaume Baverez","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-21T14:46:03Z","title":"Higher equations of motion at level 2 in Liouville CFT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13900","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":"sha256:803e3fe84fe59147d4ee89275f3a7026e2aaea729d0b0a60ab72d5f98890a631","target":"record","created_at":"2026-05-20T14:03:17Z","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":"2dc2dc69b6b993dc6861e66524447fa1de55081bc003746c91114bbb8e060c42","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-21T14:46:03Z","title_canon_sha256":"5c23645b4c27cee4fd63ed4038eece55cff9e0f7a3888c2ee679093992c1c457"},"schema_version":"1.0","source":{"id":"2312.13900","kind":"arxiv","version":2}},"canonical_sha256":"50879036d4a1f2f4f503d547b209a137abd37296c5c24e2f5772276001b3efd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50879036d4a1f2f4f503d547b209a137abd37296c5c24e2f5772276001b3efd2","first_computed_at":"2026-05-20T14:03:17.070752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T14:03:17.070752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6/KW0xxwvyygQdNxofYf950YyIBrKauuuMlRaESacChZY1GFIVQHRnpCoKGuToELuI60TgBCOr/SkX48SSZGCg==","signature_status":"signed_v1","signed_at":"2026-05-20T14:03:17.071231Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.13900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:803e3fe84fe59147d4ee89275f3a7026e2aaea729d0b0a60ab72d5f98890a631","sha256:ad62c403361394c98567e2f5a59ba5162be34080994e92a31e063f060db33fff"],"state_sha256":"5b4127222e035b7b943f0ac648946590a35d70e5fcc797fbae00d14c35806b9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQgna32RwWAsaSonj10xLjweINHatuzZE+I8xBaWGhKSCYCLv8SBBwGs2SOV9bHMS3CJ9r4uJ7jAprsTPWbGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:27:58.297787Z","bundle_sha256":"745795deb4f0b5d105266df144abf022c990fe1041f79db612bde25621a0a83c"}}