{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UHI7DVFN5JO5KYSRV2UFMMP33L","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":"333adf816ed32f188d1190856d955b0a2963ba0cb63bad071e66d1d0f95c0013","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-15T12:16:55Z","title_canon_sha256":"46b07e3472a1c713d02b2dd61dcf54ab9fd542d88c56d42fbe9afef1f5d104b5"},"schema_version":"1.0","source":{"id":"1805.05724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05724","created_at":"2026-05-18T00:15:53Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05724v1","created_at":"2026-05-18T00:15:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05724","created_at":"2026-05-18T00:15:53Z"},{"alias_kind":"pith_short_12","alias_value":"UHI7DVFN5JO5","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UHI7DVFN5JO5KYSR","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UHI7DVFN","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:b25756b9615e0e96f5f78d92356bbee8036df8ce78f8ed8b9a60f7183f8f799a","target":"graph","created_at":"2026-05-18T00:15:53Z","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":"In this paper we study simple transitive $2$-representations of certain $2$-subcategories of the $2$-category of projective functors over a star algebra. We show that in the simplest case, which is associated to the Dynkin type $A_2$, simple transitive $2$-representations are classified by cell $2$-representations. In the general case we conjecture that there exist many simple transitive $2$-representations which are not cell $2$-representations and provide some evidence for our conjecture.","authors_text":"Jakob Zimmermann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-15T12:16:55Z","title":"Simple transitive $2$-representations of left cell $2$-subcategories of projective functors for star algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05724","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:a91d4bc3b9bd393f747070b264154b04e63e9f05c4c5b7bdc10c818cdf862347","target":"record","created_at":"2026-05-18T00:15:53Z","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":"333adf816ed32f188d1190856d955b0a2963ba0cb63bad071e66d1d0f95c0013","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-15T12:16:55Z","title_canon_sha256":"46b07e3472a1c713d02b2dd61dcf54ab9fd542d88c56d42fbe9afef1f5d104b5"},"schema_version":"1.0","source":{"id":"1805.05724","kind":"arxiv","version":1}},"canonical_sha256":"a1d1f1d4adea5dd56251aea85631fbdac5af3aa90005825c7210f2f1654e4ccf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1d1f1d4adea5dd56251aea85631fbdac5af3aa90005825c7210f2f1654e4ccf","first_computed_at":"2026-05-18T00:15:53.883011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:53.883011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"32yYzZRUDpwism0Yzrlw+OjwuKt/EyZf3RnKBdYvRRIwVSXBQ2R2G99SG9rE5rJ2LEziLhWiWhIlLzmCxsT7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:53.883746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a91d4bc3b9bd393f747070b264154b04e63e9f05c4c5b7bdc10c818cdf862347","sha256:b25756b9615e0e96f5f78d92356bbee8036df8ce78f8ed8b9a60f7183f8f799a"],"state_sha256":"ee4a72a31558334bac7040fd393f9532cbba94c52e351fa0782c0e8d20a379e6"}