{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UHI7DVFN5JO5KYSRV2UFMMP33L","short_pith_number":"pith:UHI7DVFN","schema_version":"1.0","canonical_sha256":"a1d1f1d4adea5dd56251aea85631fbdac5af3aa90005825c7210f2f1654e4ccf","source":{"kind":"arxiv","id":"1805.05724","version":1},"attestation_state":"computed","paper":{"title":"Simple transitive $2$-representations of left cell $2$-subcategories of projective functors for star algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jakob Zimmermann","submitted_at":"2018-05-15T12:16:55Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.05724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-15T12:16:55Z","cross_cats_sorted":[],"title_canon_sha256":"46b07e3472a1c713d02b2dd61dcf54ab9fd542d88c56d42fbe9afef1f5d104b5","abstract_canon_sha256":"333adf816ed32f188d1190856d955b0a2963ba0cb63bad071e66d1d0f95c0013"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:53.883746Z","signature_b64":"32yYzZRUDpwism0Yzrlw+OjwuKt/EyZf3RnKBdYvRRIwVSXBQ2R2G99SG9rE5rJ2LEziLhWiWhIlLzmCxsT7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1d1f1d4adea5dd56251aea85631fbdac5af3aa90005825c7210f2f1654e4ccf","last_reissued_at":"2026-05-18T00:15:53.883011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:53.883011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple transitive $2$-representations of left cell $2$-subcategories of projective functors for star algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jakob Zimmermann","submitted_at":"2018-05-15T12:16:55Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05724","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.05724","created_at":"2026-05-18T00:15:53.883140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.05724v1","created_at":"2026-05-18T00:15:53.883140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05724","created_at":"2026-05-18T00:15:53.883140+00:00"},{"alias_kind":"pith_short_12","alias_value":"UHI7DVFN5JO5","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UHI7DVFN5JO5KYSR","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UHI7DVFN","created_at":"2026-05-18T12:32:56.356000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L","json":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L.json","graph_json":"https://pith.science/api/pith-number/UHI7DVFN5JO5KYSRV2UFMMP33L/graph.json","events_json":"https://pith.science/api/pith-number/UHI7DVFN5JO5KYSRV2UFMMP33L/events.json","paper":"https://pith.science/paper/UHI7DVFN"},"agent_actions":{"view_html":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L","download_json":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L.json","view_paper":"https://pith.science/paper/UHI7DVFN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.05724&json=true","fetch_graph":"https://pith.science/api/pith-number/UHI7DVFN5JO5KYSRV2UFMMP33L/graph.json","fetch_events":"https://pith.science/api/pith-number/UHI7DVFN5JO5KYSRV2UFMMP33L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L/action/storage_attestation","attest_author":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L/action/author_attestation","sign_citation":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L/action/citation_signature","submit_replication":"https://pith.science/pith/UHI7DVFN5JO5KYSRV2UFMMP33L/action/replication_record"}},"created_at":"2026-05-18T00:15:53.883140+00:00","updated_at":"2026-05-18T00:15:53.883140+00:00"}