{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:444WNBW5AWCOW55G34G67GIYPK","short_pith_number":"pith:444WNBW5","schema_version":"1.0","canonical_sha256":"e7396686dd0584eb77a6df0def99187a9589acbace0468fdabf8fb66651b789a","source":{"kind":"arxiv","id":"2409.01406","version":2},"attestation_state":"computed","paper":{"title":"Mutual information from modular flow in CFTs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Cesar A. Agon, Guim Planella Planas, Horacio Casini, Umut G\\\"ursoy","submitted_at":"2024-09-02T18:01:55Z","abstract_excerpt":"The operator product expansion (OPE) of twist operators in the replica trick framework enables a long-distance expansion of the mutual information (MI) in conformal field theories (CFTs). In this expansion, the terms are labeled by primary operators, as contributions from descendant operators can be resummed into conformal blocks. However, for the MI, the expansion involves primaries from the multi-replica theory, which includes far more operators than those in the original theory. In this work, we develop a method to resum this series, yielding an expansion in terms of the primaries of the or"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2409.01406","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-09-02T18:01:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5237c581922d7fc3e8e83cfd9a2251a48609983f127877d28e1313084bbd1189","abstract_canon_sha256":"3b76b94b58a1f94e563b0f0cf8afda19b5a4e5389c920c33d09acd0d639dc7c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:04:28.022986Z","signature_b64":"lfjEVQZb5HocABNYP33c7GwYIe5+C1CwX74ceKjAbTVR0t2lOMgK7P1gIkNsu/SXlkKCqirlL3FOQEEPDyqDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7396686dd0584eb77a6df0def99187a9589acbace0468fdabf8fb66651b789a","last_reissued_at":"2026-07-05T12:04:28.022464Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:04:28.022464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mutual information from modular flow in CFTs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Cesar A. Agon, Guim Planella Planas, Horacio Casini, Umut G\\\"ursoy","submitted_at":"2024-09-02T18:01:55Z","abstract_excerpt":"The operator product expansion (OPE) of twist operators in the replica trick framework enables a long-distance expansion of the mutual information (MI) in conformal field theories (CFTs). In this expansion, the terms are labeled by primary operators, as contributions from descendant operators can be resummed into conformal blocks. However, for the MI, the expansion involves primaries from the multi-replica theory, which includes far more operators than those in the original theory. In this work, we develop a method to resum this series, yielding an expansion in terms of the primaries of the or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01406","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/2409.01406/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2409.01406","created_at":"2026-07-05T12:04:28.022529+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.01406v2","created_at":"2026-07-05T12:04:28.022529+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01406","created_at":"2026-07-05T12:04:28.022529+00:00"},{"alias_kind":"pith_short_12","alias_value":"444WNBW5AWCO","created_at":"2026-07-05T12:04:28.022529+00:00"},{"alias_kind":"pith_short_16","alias_value":"444WNBW5AWCOW55G","created_at":"2026-07-05T12:04:28.022529+00:00"},{"alias_kind":"pith_short_8","alias_value":"444WNBW5","created_at":"2026-07-05T12:04:28.022529+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.19860","citing_title":"Mutual Information from Modular Flow in General CFTs","ref_index":22,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK","json":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK.json","graph_json":"https://pith.science/api/pith-number/444WNBW5AWCOW55G34G67GIYPK/graph.json","events_json":"https://pith.science/api/pith-number/444WNBW5AWCOW55G34G67GIYPK/events.json","paper":"https://pith.science/paper/444WNBW5"},"agent_actions":{"view_html":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK","download_json":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK.json","view_paper":"https://pith.science/paper/444WNBW5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.01406&json=true","fetch_graph":"https://pith.science/api/pith-number/444WNBW5AWCOW55G34G67GIYPK/graph.json","fetch_events":"https://pith.science/api/pith-number/444WNBW5AWCOW55G34G67GIYPK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK/action/storage_attestation","attest_author":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK/action/author_attestation","sign_citation":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK/action/citation_signature","submit_replication":"https://pith.science/pith/444WNBW5AWCOW55G34G67GIYPK/action/replication_record"}},"created_at":"2026-07-05T12:04:28.022529+00:00","updated_at":"2026-07-05T12:04:28.022529+00:00"}