{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NOGAVZNOAVHWGASW2IMI7ID5LD","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":"20bf7523c71d0224de09506fc3803f51888e6d0e48d85094d208aa534ff18bfb","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-10-20T01:52:27Z","title_canon_sha256":"14a4ddb05efad59b50c444e9516173d09ee44b1344353a21a79af9b771cc65a7"},"schema_version":"1.0","source":{"id":"2110.10336","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.10336","created_at":"2026-07-05T05:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2110.10336v1","created_at":"2026-07-05T05:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.10336","created_at":"2026-07-05T05:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"NOGAVZNOAVHW","created_at":"2026-07-05T05:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"NOGAVZNOAVHWGASW","created_at":"2026-07-05T05:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"NOGAVZNO","created_at":"2026-07-05T05:06:08Z"}],"graph_snapshots":[{"event_id":"sha256:34811bf3e854a54dbb0afe453c5e45da1a87732a8da3bfbca662470be904c8d0","target":"graph","created_at":"2026-07-05T05:06:08Z","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/2110.10336/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Bershadsky-Polyakov algebras are the original examples of nonregular W-algebras, obtained from the affine vertex operator algebras associated with $\\mathfrak{sl}_3$ by quantum hamiltonian reduction. In [arXiv:2007.03917], we explored the representation theories of the simple quotients of these algebras when the level $\\mathsf{k}$ is nondegenerate-admissible. Here, we combine these explorations with Adamovi\\'{c}'s inverse quantum hamiltonian reduction functors to study the modular properties of Bershadsky-Polyakov characters and deduce the associated Grothendieck fusion rules. The results a","authors_text":"David Ridout, Zachary Fehily","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-10-20T01:52:27Z","title":"Modularity of Bershadsky-Polyakov minimal models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10336","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:e6434bc392961a7a2ea005f281b5af7e2b6ff77bdb25c1d955dc6eea5aa6c2a2","target":"record","created_at":"2026-07-05T05:06:08Z","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":"20bf7523c71d0224de09506fc3803f51888e6d0e48d85094d208aa534ff18bfb","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-10-20T01:52:27Z","title_canon_sha256":"14a4ddb05efad59b50c444e9516173d09ee44b1344353a21a79af9b771cc65a7"},"schema_version":"1.0","source":{"id":"2110.10336","kind":"arxiv","version":1}},"canonical_sha256":"6b8c0ae5ae054f630256d2188fa07d58d13d1eb7ea328c98e28b70655150c48c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b8c0ae5ae054f630256d2188fa07d58d13d1eb7ea328c98e28b70655150c48c","first_computed_at":"2026-07-05T05:06:08.641237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:08.641237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RfGQvX74qZvIrodKJyb2ON3OPYw2N9wCpJOjd0fAM0osB9Fb6AQDMxE4tNBFekBD4NI63UMvL1ZV7A4WV403Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:08.641814Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.10336","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6434bc392961a7a2ea005f281b5af7e2b6ff77bdb25c1d955dc6eea5aa6c2a2","sha256:34811bf3e854a54dbb0afe453c5e45da1a87732a8da3bfbca662470be904c8d0"],"state_sha256":"cd29545f05d72b1f1b912be9aa0878b198c5b57e52eb6b2455ca2e4f649b303a"}