{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HXE2ZBTG6JDPAUHERCVD5VO3EU","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":"b7854b6aa4b5c90f27855cd0cab4c80d2ad9a25c88eefc7b6f9fba396443951e","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-02T11:29:13Z","title_canon_sha256":"554f17954fe717d7600874c2570304bc63234d0dd7ae759551a718d0c31ee784"},"schema_version":"1.0","source":{"id":"1409.0670","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0670","created_at":"2026-05-18T01:42:10Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0670v3","created_at":"2026-05-18T01:42:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0670","created_at":"2026-05-18T01:42:10Z"},{"alias_kind":"pith_short_12","alias_value":"HXE2ZBTG6JDP","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HXE2ZBTG6JDPAUHE","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HXE2ZBTG","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:8ac0f9c5d843a2ca14f98bdcec803e2796cc4df2db2ea385af81bc6f817da4ab","target":"graph","created_at":"2026-05-18T01:42:10Z","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"},"paper":{"abstract_excerpt":"In rational conformal field theory, the Verlinde formula computes the fusion coefficients from the modular S-transformations of the characters of the chiral algebra's representations. Generalising this formula to logarithmic models has proven rather difficult for a variety of reasons. Here, a recently proposed formalism (arXiv:1303.0847 [hep-th]) for the modular properties of certain classes of logarithmic theories is reviewed, and refined, using simple examples. A formalism addressing fusion rules in simple current extensions is also reviewed as a means to tackle logarithmic theories to which","authors_text":"David Ridout, Simon Wood","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-02T11:29:13Z","title":"The Verlinde formula in logarithmic CFT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0670","kind":"arxiv","version":3},"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:c3e44df7c7ed25e040edaf77c15313c704be53be6c4bcc687de4205bb443df91","target":"record","created_at":"2026-05-18T01:42:10Z","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":"b7854b6aa4b5c90f27855cd0cab4c80d2ad9a25c88eefc7b6f9fba396443951e","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-02T11:29:13Z","title_canon_sha256":"554f17954fe717d7600874c2570304bc63234d0dd7ae759551a718d0c31ee784"},"schema_version":"1.0","source":{"id":"1409.0670","kind":"arxiv","version":3}},"canonical_sha256":"3dc9ac8666f246f050e488aa3ed5db251091a6178a9dd9b1a4e94bd28f3c7fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dc9ac8666f246f050e488aa3ed5db251091a6178a9dd9b1a4e94bd28f3c7fd4","first_computed_at":"2026-05-18T01:42:10.849457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:10.849457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5VY3RHIul8PbNrYvx/ZmxPAcZW7gVppd888ZASpP0N0xjZrjIzq+jjh7axwIEzTBc72obwsJZou11kOF9RIvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:10.849963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0670","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3e44df7c7ed25e040edaf77c15313c704be53be6c4bcc687de4205bb443df91","sha256:8ac0f9c5d843a2ca14f98bdcec803e2796cc4df2db2ea385af81bc6f817da4ab"],"state_sha256":"46419a418642260a816597aa0c72edf49cb8e3c0769e8d417aaeafcd27b0a9ca"}