{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:KCA45ZSZT3NJZIH4P3VHNR45X2","short_pith_number":"pith:KCA45ZSZ","canonical_record":{"source":{"id":"hep-th/0403157","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-03-15T19:37:46Z","cross_cats_sorted":["math.CT","math.QA"],"title_canon_sha256":"d60b01fc8edfd66ab4fd98a20101cca0bfdb1947c2257ef9c9b7e9b082eb479b","abstract_canon_sha256":"409eab8e9e2c27f5ab4d85a8758e31fe2fee601dabc69f4fd2d97db4425b2f8c"},"schema_version":"1.0"},"canonical_sha256":"5081cee6599eda9ca0fc7eea76c79dbeb91c3270e3650d59c61c87366a86b0a4","source":{"kind":"arxiv","id":"hep-th/0403157","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0403157","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0403157v2","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0403157","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"KCA45ZSZT3NJ","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"pith_short_16","alias_value":"KCA45ZSZT3NJZIH4","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"pith_short_8","alias_value":"KCA45ZSZ","created_at":"2026-07-04T17:24:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:KCA45ZSZT3NJZIH4P3VHNR45X2","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0403157","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-03-15T19:37:46Z","cross_cats_sorted":["math.CT","math.QA"],"title_canon_sha256":"d60b01fc8edfd66ab4fd98a20101cca0bfdb1947c2257ef9c9b7e9b082eb479b","abstract_canon_sha256":"409eab8e9e2c27f5ab4d85a8758e31fe2fee601dabc69f4fd2d97db4425b2f8c"},"schema_version":"1.0"},"canonical_sha256":"5081cee6599eda9ca0fc7eea76c79dbeb91c3270e3650d59c61c87366a86b0a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:24:44.303275Z","signature_b64":"7Ukc5Vve5G7x6sxNQyo+rSxQjfLNfLAWduMv9nYQK7zDublmFz+VwYQTx07z4XEs4hL3A5SRbWwrzxO+zBimAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5081cee6599eda9ca0fc7eea76c79dbeb91c3270e3650d59c61c87366a86b0a4","last_reissued_at":"2026-07-04T17:24:44.302940Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:24:44.302940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0403157","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":"2026-07-04T17:24:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pg1LUkN0vSV/8I+UxhauU2sTIv4eiSyaPiomUqeykoJDXdLPn4kQ0/vx2C2v+6sG+/UybeWa4KYA1Q3OTw1UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:48:40.658740Z"},"content_sha256":"cf323b37abb3354318011433279da2dfd48b9dbce2e4692064732c659c8cde3f","schema_version":"1.0","event_id":"sha256:cf323b37abb3354318011433279da2dfd48b9dbce2e4692064732c659c8cde3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:KCA45ZSZT3NJZIH4P3VHNR45X2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"TFT construction of RCFT correlators III: Simple currents","license":"","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"hep-th","authors_text":"Christoph Schweigert, Ingo Runkel, Juergen Fuchs","submitted_at":"2004-03-15T19:37:46Z","abstract_excerpt":"We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer and Schellekens. We also classify boundary conditions in the associated conformal field theories and show that the boundary states are given by the formula proposed in hep-th/0007174. Finally, we investigate conformal defects in these theories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0403157","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/hep-th/0403157/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":"2026-07-04T17:24:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aUKuw8wvPGzSXRCOURFQsvyZhiX08iqqY7hALILuaPaR0jaW5O44Cs9L+VrPVGrfP9/FEnfH+QCMv4pBHVIVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:48:40.659263Z"},"content_sha256":"5b46e2fec67f71862fc7369a2890332d31cd7d447e6717cecc75020a235947b8","schema_version":"1.0","event_id":"sha256:5b46e2fec67f71862fc7369a2890332d31cd7d447e6717cecc75020a235947b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCA45ZSZT3NJZIH4P3VHNR45X2/bundle.json","state_url":"https://pith.science/pith/KCA45ZSZT3NJZIH4P3VHNR45X2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCA45ZSZT3NJZIH4P3VHNR45X2/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":"2026-08-03T15:48:40Z","links":{"resolver":"https://pith.science/pith/KCA45ZSZT3NJZIH4P3VHNR45X2","bundle":"https://pith.science/pith/KCA45ZSZT3NJZIH4P3VHNR45X2/bundle.json","state":"https://pith.science/pith/KCA45ZSZT3NJZIH4P3VHNR45X2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCA45ZSZT3NJZIH4P3VHNR45X2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:KCA45ZSZT3NJZIH4P3VHNR45X2","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":"409eab8e9e2c27f5ab4d85a8758e31fe2fee601dabc69f4fd2d97db4425b2f8c","cross_cats_sorted":["math.CT","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2004-03-15T19:37:46Z","title_canon_sha256":"d60b01fc8edfd66ab4fd98a20101cca0bfdb1947c2257ef9c9b7e9b082eb479b"},"schema_version":"1.0","source":{"id":"hep-th/0403157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0403157","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0403157v2","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0403157","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"KCA45ZSZT3NJ","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"pith_short_16","alias_value":"KCA45ZSZT3NJZIH4","created_at":"2026-07-04T17:24:44Z"},{"alias_kind":"pith_short_8","alias_value":"KCA45ZSZ","created_at":"2026-07-04T17:24:44Z"}],"graph_snapshots":[{"event_id":"sha256:5b46e2fec67f71862fc7369a2890332d31cd7d447e6717cecc75020a235947b8","target":"graph","created_at":"2026-07-04T17:24:44Z","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/hep-th/0403157/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer and Schellekens. We also classify boundary conditions in the associated conformal field theories and show that the boundary states are given by the formula proposed in hep-th/0007174. Finally, we investigate conformal defects in these theories.","authors_text":"Christoph Schweigert, Ingo Runkel, Juergen Fuchs","cross_cats":["math.CT","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2004-03-15T19:37:46Z","title":"TFT construction of RCFT correlators III: Simple currents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0403157","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:cf323b37abb3354318011433279da2dfd48b9dbce2e4692064732c659c8cde3f","target":"record","created_at":"2026-07-04T17:24:44Z","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":"409eab8e9e2c27f5ab4d85a8758e31fe2fee601dabc69f4fd2d97db4425b2f8c","cross_cats_sorted":["math.CT","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2004-03-15T19:37:46Z","title_canon_sha256":"d60b01fc8edfd66ab4fd98a20101cca0bfdb1947c2257ef9c9b7e9b082eb479b"},"schema_version":"1.0","source":{"id":"hep-th/0403157","kind":"arxiv","version":2}},"canonical_sha256":"5081cee6599eda9ca0fc7eea76c79dbeb91c3270e3650d59c61c87366a86b0a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5081cee6599eda9ca0fc7eea76c79dbeb91c3270e3650d59c61c87366a86b0a4","first_computed_at":"2026-07-04T17:24:44.302940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:24:44.302940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Ukc5Vve5G7x6sxNQyo+rSxQjfLNfLAWduMv9nYQK7zDublmFz+VwYQTx07z4XEs4hL3A5SRbWwrzxO+zBimAw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:24:44.303275Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0403157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf323b37abb3354318011433279da2dfd48b9dbce2e4692064732c659c8cde3f","sha256:5b46e2fec67f71862fc7369a2890332d31cd7d447e6717cecc75020a235947b8"],"state_sha256":"ef092aac57b5499e98ebd8bad5a8e084163ce30eafa964578ee56d98ea52d3ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTn11jS4kML3+8Im+DAcIIvpeCGd0S0q3nZPDzOe2w2kr72xreev/Tt7uC5ulXGrP0fPQotk9WGvF9CCDct8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T15:48:40.662590Z","bundle_sha256":"5963150b0eed12d7a1a99fae72162bde766580619b3403ab8c9ee7e7d2f6411b"}}