{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XBEBFDIDJMHYENSXSTZXVOIIMC","short_pith_number":"pith:XBEBFDID","schema_version":"1.0","canonical_sha256":"b848128d034b0f82365794f37ab908609365c602f03a2398c540ea250ed9c188","source":{"kind":"arxiv","id":"1612.05182","version":2},"attestation_state":"computed","paper":{"title":"Jellyfish partition categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Comes","submitted_at":"2016-12-15T18:28:25Z","abstract_excerpt":"For each positive integer $n$, we introduce a monoidal category $\\mathcal{JP}(n)$ using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least $n$, we show $\\mathcal{JP}(n)$ is monoidally equivalent to the full subcategory of $\\operatorname{Rep}(A_n)$ whose objects are tensor powers of the natural $n$-dimensional permutation representation of the alternating group $A_n$."},"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":"1612.05182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-15T18:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"42de811f7f0c622b43202d76ac7fe53300c8369991a46fb13cc3a97a486553b8","abstract_canon_sha256":"db9e55206106c59be0db20d6cd7b64fac465322560380dacfb802ee8a6f304a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:05.561413Z","signature_b64":"xVUdMMFu07z0zrCBopNOV4bNhuY8PshcjAmN2rSDFGcFnyco72GcPtWQPlcqg7Q2349tIZW3MjDMkHo5reaHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b848128d034b0f82365794f37ab908609365c602f03a2398c540ea250ed9c188","last_reissued_at":"2026-05-18T00:51:05.561007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:05.561007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jellyfish partition categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Comes","submitted_at":"2016-12-15T18:28:25Z","abstract_excerpt":"For each positive integer $n$, we introduce a monoidal category $\\mathcal{JP}(n)$ using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least $n$, we show $\\mathcal{JP}(n)$ is monoidally equivalent to the full subcategory of $\\operatorname{Rep}(A_n)$ whose objects are tensor powers of the natural $n$-dimensional permutation representation of the alternating group $A_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05182","kind":"arxiv","version":2},"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":"1612.05182","created_at":"2026-05-18T00:51:05.561069+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.05182v2","created_at":"2026-05-18T00:51:05.561069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05182","created_at":"2026-05-18T00:51:05.561069+00:00"},{"alias_kind":"pith_short_12","alias_value":"XBEBFDIDJMHY","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XBEBFDIDJMHYENSX","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XBEBFDID","created_at":"2026-05-18T12:30:51.357362+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/XBEBFDIDJMHYENSXSTZXVOIIMC","json":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC.json","graph_json":"https://pith.science/api/pith-number/XBEBFDIDJMHYENSXSTZXVOIIMC/graph.json","events_json":"https://pith.science/api/pith-number/XBEBFDIDJMHYENSXSTZXVOIIMC/events.json","paper":"https://pith.science/paper/XBEBFDID"},"agent_actions":{"view_html":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC","download_json":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC.json","view_paper":"https://pith.science/paper/XBEBFDID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.05182&json=true","fetch_graph":"https://pith.science/api/pith-number/XBEBFDIDJMHYENSXSTZXVOIIMC/graph.json","fetch_events":"https://pith.science/api/pith-number/XBEBFDIDJMHYENSXSTZXVOIIMC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/action/storage_attestation","attest_author":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/action/author_attestation","sign_citation":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/action/citation_signature","submit_replication":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/action/replication_record"}},"created_at":"2026-05-18T00:51:05.561069+00:00","updated_at":"2026-05-18T00:51:05.561069+00:00"}