{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GQMJGT66OZ2POFW3CSIRLEDWNQ","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":"ed2a308eda3d6b6c4ae935f26635791664dca5c28208826d38ecf2784dfde9a4","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-27T19:05:28Z","title_canon_sha256":"d757240d1aacdf2fd2e14a6cd0b5d89e8c0f9efd897c9dbbcfd897c7b802a235"},"schema_version":"1.0","source":{"id":"2411.18696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18696","created_at":"2026-07-05T11:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18696v2","created_at":"2026-07-05T11:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18696","created_at":"2026-07-05T11:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"GQMJGT66OZ2P","created_at":"2026-07-05T11:33:48Z"},{"alias_kind":"pith_short_16","alias_value":"GQMJGT66OZ2POFW3","created_at":"2026-07-05T11:33:48Z"},{"alias_kind":"pith_short_8","alias_value":"GQMJGT66","created_at":"2026-07-05T11:33:48Z"}],"graph_snapshots":[{"event_id":"sha256:30b08605ca3d2df2df2e360f636f0bf31dda59cf5134ece87a756ff1f6678de0","target":"graph","created_at":"2026-07-05T11:33:48Z","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/2411.18696/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study Kac operators (e.g. energy operator) in percolation and self-avoiding walk bulk CFTs with central charge $c=0$. The proper normalizations of these operators can be deduced at generic $c$ by requiring the finiteness and reality of the three-point constants in cluster and loop model CFTs. At $c=0$, Kac operators become zero-norm states and the bottom fields of logarithmic multiplets, and comparison with $c<1$ Liouville CFT suggests the potential existence of arbitrarily high rank Jordan blocks. We give a generic construction of logarithmic operators based on Kac operators and focus on t","authors_text":"Yifei He","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-27T19:05:28Z","title":"Logarithmic operators in $c=0$ bulk CFTs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18696","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:e6f5a1bc1001fe7f6753522e2c6e5349b6ee893240602c9658c2ce9cf5f12810","target":"record","created_at":"2026-07-05T11:33:48Z","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":"ed2a308eda3d6b6c4ae935f26635791664dca5c28208826d38ecf2784dfde9a4","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-11-27T19:05:28Z","title_canon_sha256":"d757240d1aacdf2fd2e14a6cd0b5d89e8c0f9efd897c9dbbcfd897c7b802a235"},"schema_version":"1.0","source":{"id":"2411.18696","kind":"arxiv","version":2}},"canonical_sha256":"3418934fde7674f716db14911590766c05605e23c7d6968ef0ecc18e6d5e9d07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3418934fde7674f716db14911590766c05605e23c7d6968ef0ecc18e6d5e9d07","first_computed_at":"2026-07-05T11:33:48.212578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:48.212578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WUEcH/oDNv+BwIRj8gVXyz1XgpbwGS43mwtzqk8yu3Ym+gdr+iHJInGwS5L92XGrbIx5NZeCn/y93Ml4ioGHDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:48.213003Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6f5a1bc1001fe7f6753522e2c6e5349b6ee893240602c9658c2ce9cf5f12810","sha256:30b08605ca3d2df2df2e360f636f0bf31dda59cf5134ece87a756ff1f6678de0"],"state_sha256":"42e2730932b551b914609124e5f7f9585f73ce49aedebff19c1dbcee3bf29035"}