{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:T65EEOCZZ4TPIM54KDAFLWFCWN","short_pith_number":"pith:T65EEOCZ","schema_version":"1.0","canonical_sha256":"9fba423859cf26f433bc50c055d8a2b36b8a85a799088cd9738bb4874bd164bd","source":{"kind":"arxiv","id":"1309.3510","version":1},"attestation_state":"computed","paper":{"title":"Centralizers of the infinite symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Peter Herbrich, Zajj Daugherty","submitted_at":"2013-09-13T17:04:09Z","abstract_excerpt":"We review and introduce several approaches to the study of centralizer algebras of the infinite symmetric group $S_\\infty$. Our study is led by the double commutant relationships between finite symmetric groups and partition algebras; each approach produces a centralizer algebra that is contained in a partition algebra. Our goal is to incorporate invariants of $S_\\infty$, which ties our work to the study of symmetric functions in non-commuting variables. We resultantly explore sequence spaces as permutation modules, which yields families of non-unitary representations of $S_\\infty$."},"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":"1309.3510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-13T17:04:09Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"03f7a8f2aeb51c38e622139feab2464408eadbcbe40bb529eecdbea65fadf24b","abstract_canon_sha256":"9c95e6d9fc5a2dfa8393d8542221cadb24df5b539fa7d5f8ba7bf91cae685e64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:22.390384Z","signature_b64":"B34wogNBRPo2z/qNWGS+MMK9nky8mOsTNnlIgjF/kWyonyKE1VQsGECt7eas+28VVnMQeKgh+aarVtZr0YkfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fba423859cf26f433bc50c055d8a2b36b8a85a799088cd9738bb4874bd164bd","last_reissued_at":"2026-05-18T03:13:22.389953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:22.389953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Centralizers of the infinite symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Peter Herbrich, Zajj Daugherty","submitted_at":"2013-09-13T17:04:09Z","abstract_excerpt":"We review and introduce several approaches to the study of centralizer algebras of the infinite symmetric group $S_\\infty$. Our study is led by the double commutant relationships between finite symmetric groups and partition algebras; each approach produces a centralizer algebra that is contained in a partition algebra. Our goal is to incorporate invariants of $S_\\infty$, which ties our work to the study of symmetric functions in non-commuting variables. We resultantly explore sequence spaces as permutation modules, which yields families of non-unitary representations of $S_\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3510","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":"1309.3510","created_at":"2026-05-18T03:13:22.390017+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.3510v1","created_at":"2026-05-18T03:13:22.390017+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3510","created_at":"2026-05-18T03:13:22.390017+00:00"},{"alias_kind":"pith_short_12","alias_value":"T65EEOCZZ4TP","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"T65EEOCZZ4TPIM54","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"T65EEOCZ","created_at":"2026-05-18T12:27:59.945178+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/T65EEOCZZ4TPIM54KDAFLWFCWN","json":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN.json","graph_json":"https://pith.science/api/pith-number/T65EEOCZZ4TPIM54KDAFLWFCWN/graph.json","events_json":"https://pith.science/api/pith-number/T65EEOCZZ4TPIM54KDAFLWFCWN/events.json","paper":"https://pith.science/paper/T65EEOCZ"},"agent_actions":{"view_html":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN","download_json":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN.json","view_paper":"https://pith.science/paper/T65EEOCZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.3510&json=true","fetch_graph":"https://pith.science/api/pith-number/T65EEOCZZ4TPIM54KDAFLWFCWN/graph.json","fetch_events":"https://pith.science/api/pith-number/T65EEOCZZ4TPIM54KDAFLWFCWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN/action/storage_attestation","attest_author":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN/action/author_attestation","sign_citation":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN/action/citation_signature","submit_replication":"https://pith.science/pith/T65EEOCZZ4TPIM54KDAFLWFCWN/action/replication_record"}},"created_at":"2026-05-18T03:13:22.390017+00:00","updated_at":"2026-05-18T03:13:22.390017+00:00"}