{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:HIYVPA3MM6DP4SCUJ4DPB334NT","short_pith_number":"pith:HIYVPA3M","schema_version":"1.0","canonical_sha256":"3a3157836c6786fe48544f06f0ef7c6ce1189c32223fc422eaa7b750d191ba06","source":{"kind":"arxiv","id":"2107.05099","version":1},"attestation_state":"computed","paper":{"title":"A new approach to the representation theory of the partition category","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Brundan, Max Vargas","submitted_at":"2021-07-11T17:38:50Z","abstract_excerpt":"We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by Enyang. Our reformulation involves a new graphical monoidal category, the affine partition category, which is defined here as a certain monoidal subcategory of Khovanov's Heisenberg category. We use the Jucys-Murphy elements to construct some special projective functors, then apply these functors to give self-contained proofs of results of Comes and Ostrik on blocks of Deligne"},"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":"2107.05099","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-07-11T17:38:50Z","cross_cats_sorted":[],"title_canon_sha256":"080f6aa0596b95e6d82aeb3666ac5d89a09be1202a5a5317c95a0dee1339a617","abstract_canon_sha256":"aba71b928235ddd885e392e1d56131ce5b72258500763bb3e567b4e7af112f08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:49:38.928764Z","signature_b64":"bRHs6xfCGYUsYy8pEu5sQn+gKpOhC0EcC/tm3AVsBaPO8B4JrKFPoKgVy8/lYPUc7ud55wYc0Jg/dYWJJ9NECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a3157836c6786fe48544f06f0ef7c6ce1189c32223fc422eaa7b750d191ba06","last_reissued_at":"2026-07-05T06:49:38.928310Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:49:38.928310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new approach to the representation theory of the partition category","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Brundan, Max Vargas","submitted_at":"2021-07-11T17:38:50Z","abstract_excerpt":"We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by Enyang. Our reformulation involves a new graphical monoidal category, the affine partition category, which is defined here as a certain monoidal subcategory of Khovanov's Heisenberg category. We use the Jucys-Murphy elements to construct some special projective functors, then apply these functors to give self-contained proofs of results of Comes and Ostrik on blocks of Deligne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05099","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.05099/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2107.05099","created_at":"2026-07-05T06:49:38.928376+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.05099v1","created_at":"2026-07-05T06:49:38.928376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.05099","created_at":"2026-07-05T06:49:38.928376+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIYVPA3MM6DP","created_at":"2026-07-05T06:49:38.928376+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIYVPA3MM6DP4SCU","created_at":"2026-07-05T06:49:38.928376+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIYVPA3M","created_at":"2026-07-05T06:49:38.928376+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.05005","citing_title":"Diagrammatic Categories which arise from Representation Graphs","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT","json":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT.json","graph_json":"https://pith.science/api/pith-number/HIYVPA3MM6DP4SCUJ4DPB334NT/graph.json","events_json":"https://pith.science/api/pith-number/HIYVPA3MM6DP4SCUJ4DPB334NT/events.json","paper":"https://pith.science/paper/HIYVPA3M"},"agent_actions":{"view_html":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT","download_json":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT.json","view_paper":"https://pith.science/paper/HIYVPA3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.05099&json=true","fetch_graph":"https://pith.science/api/pith-number/HIYVPA3MM6DP4SCUJ4DPB334NT/graph.json","fetch_events":"https://pith.science/api/pith-number/HIYVPA3MM6DP4SCUJ4DPB334NT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT/action/storage_attestation","attest_author":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT/action/author_attestation","sign_citation":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT/action/citation_signature","submit_replication":"https://pith.science/pith/HIYVPA3MM6DP4SCUJ4DPB334NT/action/replication_record"}},"created_at":"2026-07-05T06:49:38.928376+00:00","updated_at":"2026-07-05T06:49:38.928376+00:00"}