{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:K3EE2VH2ZXV3EVIW6B5MBC7U6A","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":"547f95ec68e23850e136b0934144a4552e74fe6b7adda0f683830f6723c73424","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-06-28T12:33:16Z","title_canon_sha256":"fdfa8bb81b2be9991068e128d3d69af06b49b0c9a0f93c860c24bce85836ab4f"},"schema_version":"1.0","source":{"id":"hep-th/9306145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9306145","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9306145v1","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9306145","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"K3EE2VH2ZXV3","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"K3EE2VH2ZXV3EVIW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"K3EE2VH2","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:73fbbfa8f4ce596dcc3e8ad7af234dd1c042d31bda1352c71d14e3a051c0d37e","target":"graph","created_at":"2026-05-18T01:06:04Z","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":"We give a complete classification of all simple current modular invariants, extending previous results for $(\\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions.  As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal wi","authors_text":"A. N. Schellekens, M. Kreuzer","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-06-28T12:33:16Z","title":"Simple currents versus orbifolds with discrete torsion -- a complete classification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9306145","kind":"arxiv","version":1},"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":"sha256:8a58645d20c7832841934cf0e8b46f331f04e32dae6b57e74ba6474feb70f4c2","target":"record","created_at":"2026-05-18T01:06:04Z","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":"547f95ec68e23850e136b0934144a4552e74fe6b7adda0f683830f6723c73424","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-06-28T12:33:16Z","title_canon_sha256":"fdfa8bb81b2be9991068e128d3d69af06b49b0c9a0f93c860c24bce85836ab4f"},"schema_version":"1.0","source":{"id":"hep-th/9306145","kind":"arxiv","version":1}},"canonical_sha256":"56c84d54facdebb25516f07ac08bf4f0132be50eb066971392266a98d3f9a97a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56c84d54facdebb25516f07ac08bf4f0132be50eb066971392266a98d3f9a97a","first_computed_at":"2026-05-18T01:06:04.887615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:04.887615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BNl1XoXw7S4saUkli4MxVmvIDPvuFnNqDZ7mEjaUrqlE4XiT+mNCHIs6pg25wHFCkr6RWqRkowwbPoxHUebGDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:04.888435Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9306145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a58645d20c7832841934cf0e8b46f331f04e32dae6b57e74ba6474feb70f4c2","sha256:73fbbfa8f4ce596dcc3e8ad7af234dd1c042d31bda1352c71d14e3a051c0d37e"],"state_sha256":"d223a436ccdd054316309df8c0a826a436f791826fcc4e426c964a6fc2d04c41"}