{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1992:NIDRPOKAYM6WOOJ7555EDTOITL","short_pith_number":"pith:NIDRPOKA","schema_version":"1.0","canonical_sha256":"6a0717b940c33d67393fef7a41cdc89aec5ba821bcd4ab24387e044f8421ef6a","source":{"kind":"arxiv","id":"hep-th/9209043","version":1},"attestation_state":"computed","paper":{"title":"WZW Commutants, Lattices, and Level 1 Partition Functions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Terry Gannon","submitted_at":"1992-09-13T20:58:00Z","abstract_excerpt":"A natural first step in the classification of all `physical' modular invariant partition functions $\\sum N_{LR}\\,\\c_L\\,\\C_R$ lies in understanding the commutant of the modular matrices $S$ and $T$. We begin this paper extending the work of Bauer and Itzykson on the commutant from the $SU(N)$ case they consider to the case where the underlying algebra is any semi-simple Lie algebra (and the levels are arbitrary). We then use this analysis to show that the partition functions associated with even self-dual lattices span the commutant. This proves that the lattice method due to Roberts and Terao,"},"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":"hep-th/9209043","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-09-13T20:58:00Z","cross_cats_sorted":[],"title_canon_sha256":"ad414f0a42aff1fcd99fe38d362c952e51ac62afd9dcf424605a3e5b9e2029c5","abstract_canon_sha256":"e8e36446e1ac3b92d44f3822ff7887d725fadeeb5f5ca118dd94b60c5e1ba413"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:55:24.904940Z","signature_b64":"Edr4HLQOSgMDlcIfg0S8SQcd2D0+aYG1QNG7I7+YlQH6UBqGDCpMZbt5w3ONVopwf74z9wkZQH4PsJZdePiyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a0717b940c33d67393fef7a41cdc89aec5ba821bcd4ab24387e044f8421ef6a","last_reissued_at":"2026-07-04T15:55:24.904572Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:55:24.904572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"WZW Commutants, Lattices, and Level 1 Partition Functions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Terry Gannon","submitted_at":"1992-09-13T20:58:00Z","abstract_excerpt":"A natural first step in the classification of all `physical' modular invariant partition functions $\\sum N_{LR}\\,\\c_L\\,\\C_R$ lies in understanding the commutant of the modular matrices $S$ and $T$. We begin this paper extending the work of Bauer and Itzykson on the commutant from the $SU(N)$ case they consider to the case where the underlying algebra is any semi-simple Lie algebra (and the levels are arbitrary). We then use this analysis to show that the partition functions associated with even self-dual lattices span the commutant. This proves that the lattice method due to Roberts and Terao,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9209043","kind":"arxiv","version":1},"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/9209043/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":"hep-th/9209043","created_at":"2026-07-04T15:55:24.904636+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9209043v1","created_at":"2026-07-04T15:55:24.904636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9209043","created_at":"2026-07-04T15:55:24.904636+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIDRPOKAYM6W","created_at":"2026-07-04T15:55:24.904636+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIDRPOKAYM6WOOJ7","created_at":"2026-07-04T15:55:24.904636+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIDRPOKA","created_at":"2026-07-04T15:55:24.904636+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.08084","citing_title":"Fermionic CFTs from topological boundaries in abelian Chern-Simons theories","ref_index":85,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL","json":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL.json","graph_json":"https://pith.science/api/pith-number/NIDRPOKAYM6WOOJ7555EDTOITL/graph.json","events_json":"https://pith.science/api/pith-number/NIDRPOKAYM6WOOJ7555EDTOITL/events.json","paper":"https://pith.science/paper/NIDRPOKA"},"agent_actions":{"view_html":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL","download_json":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL.json","view_paper":"https://pith.science/paper/NIDRPOKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9209043&json=true","fetch_graph":"https://pith.science/api/pith-number/NIDRPOKAYM6WOOJ7555EDTOITL/graph.json","fetch_events":"https://pith.science/api/pith-number/NIDRPOKAYM6WOOJ7555EDTOITL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL/action/storage_attestation","attest_author":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL/action/author_attestation","sign_citation":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL/action/citation_signature","submit_replication":"https://pith.science/pith/NIDRPOKAYM6WOOJ7555EDTOITL/action/replication_record"}},"created_at":"2026-07-04T15:55:24.904636+00:00","updated_at":"2026-07-04T15:55:24.904636+00:00"}