{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YQBENQKMPAX7UUIHMSYUZ2QIAJ","short_pith_number":"pith:YQBENQKM","schema_version":"1.0","canonical_sha256":"c40246c14c782ffa510764b14cea0802596fc911d4f0d35e73fd63a29cde1d8e","source":{"kind":"arxiv","id":"1705.10718","version":2},"attestation_state":"computed","paper":{"title":"Hilbert series for twisted commutative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AC","authors_text":"Andrew Snowden, Steven V Sam","submitted_at":"2017-05-30T16:13:51Z","abstract_excerpt":"Suppose that for each n >= 0 we have a representation $M_n$ of the symmetric group S_n. Such sequences arise in a wide variety of contexts, and often exhibit uniformity in some way. We prove a number of general results along these lines in this paper: our prototypical theorem states that if $M_n$ can be given a suitable module structure over a twisted commutative algebra then the sequence $M_n$ follows a predictable pattern. We phrase these results precisely in the language of Hilbert series (or Poincar\\'e series, or formal characters) of modules over tca's."},"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":"1705.10718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-30T16:13:51Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"cbaa3f7741bdd1aa3dcd9867a89a6b54825a258d3bfaccc6ef7065672818991d","abstract_canon_sha256":"d0080a616346d87cb07bb4c83fd4f8e82b1f401c27acfd7d4560ed537bfe20b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:42.817460Z","signature_b64":"iXQA8h0QySg8UG4Z09y3J+ii7GghS2KDl8zY0gyTRo1iJdiVH6mo/7a00AKaLGKIcuUY5xMIRJoC92PDnzaMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c40246c14c782ffa510764b14cea0802596fc911d4f0d35e73fd63a29cde1d8e","last_reissued_at":"2026-05-18T00:24:42.816850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:42.816850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert series for twisted commutative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AC","authors_text":"Andrew Snowden, Steven V Sam","submitted_at":"2017-05-30T16:13:51Z","abstract_excerpt":"Suppose that for each n >= 0 we have a representation $M_n$ of the symmetric group S_n. Such sequences arise in a wide variety of contexts, and often exhibit uniformity in some way. We prove a number of general results along these lines in this paper: our prototypical theorem states that if $M_n$ can be given a suitable module structure over a twisted commutative algebra then the sequence $M_n$ follows a predictable pattern. We phrase these results precisely in the language of Hilbert series (or Poincar\\'e series, or formal characters) of modules over tca's."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10718","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":"1705.10718","created_at":"2026-05-18T00:24:42.816929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.10718v2","created_at":"2026-05-18T00:24:42.816929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10718","created_at":"2026-05-18T00:24:42.816929+00:00"},{"alias_kind":"pith_short_12","alias_value":"YQBENQKMPAX7","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YQBENQKMPAX7UUIH","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YQBENQKM","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2207.05860","citing_title":"A note on projective dimension over twisted commutative algebras","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ","json":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ.json","graph_json":"https://pith.science/api/pith-number/YQBENQKMPAX7UUIHMSYUZ2QIAJ/graph.json","events_json":"https://pith.science/api/pith-number/YQBENQKMPAX7UUIHMSYUZ2QIAJ/events.json","paper":"https://pith.science/paper/YQBENQKM"},"agent_actions":{"view_html":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ","download_json":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ.json","view_paper":"https://pith.science/paper/YQBENQKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.10718&json=true","fetch_graph":"https://pith.science/api/pith-number/YQBENQKMPAX7UUIHMSYUZ2QIAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/YQBENQKMPAX7UUIHMSYUZ2QIAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ/action/storage_attestation","attest_author":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ/action/author_attestation","sign_citation":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ/action/citation_signature","submit_replication":"https://pith.science/pith/YQBENQKMPAX7UUIHMSYUZ2QIAJ/action/replication_record"}},"created_at":"2026-05-18T00:24:42.816929+00:00","updated_at":"2026-05-18T00:24:42.816929+00:00"}