{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:B7YD77TFJLPWZSZEKDY72S3ETQ","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":"c00ed14357ac4f57695f5a9ccc484789cf3ad122f8f187b3215e9652ce8c2cc8","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-11-18T09:01:08Z","title_canon_sha256":"79fea42815c4299014706af089bb00450cebf8d6067a0f17401c2437d50d27ed"},"schema_version":"1.0","source":{"id":"2411.11387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.11387","created_at":"2026-07-05T09:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"2411.11387v2","created_at":"2026-07-05T09:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.11387","created_at":"2026-07-05T09:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"B7YD77TFJLPW","created_at":"2026-07-05T09:40:21Z"},{"alias_kind":"pith_short_16","alias_value":"B7YD77TFJLPWZSZE","created_at":"2026-07-05T09:40:21Z"},{"alias_kind":"pith_short_8","alias_value":"B7YD77TF","created_at":"2026-07-05T09:40:21Z"}],"graph_snapshots":[{"event_id":"sha256:8b7c7dd3b8118f93341bde27f69fe5a81ac149e035e201408c989eaf8b4c7cba","target":"graph","created_at":"2026-07-05T09:40:21Z","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/2411.11387/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the categories of weight modules over the simple $\\mathfrak{sl}(2)$ and $\\mathcal{N}=2$ superconformal vertex operator algebras at fractional admissible levels and central charges are rigid (and hence the categories of weight modules are braided ribbon categories) and that the decomposition formulae of fusion products of simple projective modules conjectured by Thomas Creutzig, David Ridout and collaborators hold (including when the decomposition involves summands that are indecomposable yet not simple). In addition to solving this old open problem, we develop new techniques for ","authors_text":"Ana Ros Camacho, Florencia Orosz Hunziker, Hiromu Nakano, Simon Wood","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-11-18T09:01:08Z","title":"Fusion rules and rigidity for weight modules over the simple admissible affine $\\mathfrak{sl}(2)$ and $\\mathcal{N}=2$ superconformal vertex operator superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11387","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:b600388930ad8dd6fb921b63a8e5cee0d1e3d6aef69f60735ed4152547271617","target":"record","created_at":"2026-07-05T09:40:21Z","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":"c00ed14357ac4f57695f5a9ccc484789cf3ad122f8f187b3215e9652ce8c2cc8","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-11-18T09:01:08Z","title_canon_sha256":"79fea42815c4299014706af089bb00450cebf8d6067a0f17401c2437d50d27ed"},"schema_version":"1.0","source":{"id":"2411.11387","kind":"arxiv","version":2}},"canonical_sha256":"0ff03ffe654adf6ccb2450f1fd4b649c12687a6342fe9fe91e3b34a3833b3519","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ff03ffe654adf6ccb2450f1fd4b649c12687a6342fe9fe91e3b34a3833b3519","first_computed_at":"2026-07-05T09:40:21.203743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:21.203743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+U0VdBC+r9snAw3BQcI4H4oYDqMXPPGiy5YvVAp8k6OyDi+7DqBJrha31ouM3YvTJUHyatV9La66DsyE5VXCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:21.205165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.11387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b600388930ad8dd6fb921b63a8e5cee0d1e3d6aef69f60735ed4152547271617","sha256:8b7c7dd3b8118f93341bde27f69fe5a81ac149e035e201408c989eaf8b4c7cba"],"state_sha256":"94545a1417d8d491f8abf1893fad107df418b4931d912e5b79f9568d998b29a4"}