{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:GBX4LVKI6IE6ZF4DCSF5IFFOH7","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":"15b236dff6e7a36229173f6612c2793122c1687aebc71bb727a7f3328f5338e6","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-08-04T18:20:20Z","title_canon_sha256":"258862cfcd4ed95305fe63b0ac4e11a1d616d0eb45537b2e05e365d5cf172c3c"},"schema_version":"1.0","source":{"id":"hep-th/9908036","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9908036","created_at":"2026-05-18T04:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9908036v3","created_at":"2026-05-18T04:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9908036","created_at":"2026-05-18T04:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"GBX4LVKI6IE6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"GBX4LVKI6IE6ZF4D","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"GBX4LVKI","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:d2a5b84c578cf66078d7137585567f892e371277c35d37fdb09ed6721605bf15","target":"graph","created_at":"2026-05-18T04:17:27Z","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 develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph $G$ to each RCFT such that the conformal boundary conditions are labelled by the nodes of $G$. This approach is carried to completion for $sl(2)$ the","authors_text":"Jean-Bernard Zuber, Paul A. Pearce, Roger E. Behrend, Valentina B. Petkova","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-08-04T18:20:20Z","title":"Boundary Conditions in Rational Conformal Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9908036","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":"sha256:38f7e9164488f43fa0954e940b16370650982c236cdd2dbfc1fcac0312510d8d","target":"record","created_at":"2026-05-18T04:17:27Z","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":"15b236dff6e7a36229173f6612c2793122c1687aebc71bb727a7f3328f5338e6","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-08-04T18:20:20Z","title_canon_sha256":"258862cfcd4ed95305fe63b0ac4e11a1d616d0eb45537b2e05e365d5cf172c3c"},"schema_version":"1.0","source":{"id":"hep-th/9908036","kind":"arxiv","version":3}},"canonical_sha256":"306fc5d548f209ec9783148bd414ae3fd4fa04b70172a84cc3900410bdc42d6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"306fc5d548f209ec9783148bd414ae3fd4fa04b70172a84cc3900410bdc42d6e","first_computed_at":"2026-05-18T04:17:27.282508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:27.282508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fnkPqCFTqvX9y2baIS5UBjk+anJEM/8vAqkn0YCg2JJimjy3d/GDu9CpBWke+0OK+fbsMwE72cojctT2OYZOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:27.283362Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9908036","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38f7e9164488f43fa0954e940b16370650982c236cdd2dbfc1fcac0312510d8d","sha256:d2a5b84c578cf66078d7137585567f892e371277c35d37fdb09ed6721605bf15"],"state_sha256":"4ad4957a4d064d14dfa47bf0f4471f3dc9dc3f5138f417a3144acdfe23825889"}