{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PLYBZUG3HMNMLDPOW53L7GQHTA","short_pith_number":"pith:PLYBZUG3","schema_version":"1.0","canonical_sha256":"7af01cd0db3b1ac58deeb776bf9a07983f5a1f7ce4e2f30cf651101b58ad51e4","source":{"kind":"arxiv","id":"1210.1854","version":2},"attestation_state":"computed","paper":{"title":"FI-modules over Noetherian rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO","math.GT"],"primary_cat":"math.RT","authors_text":"Benson Farb, Jordan S. Ellenberg, Rohit Nagpal, Thomas Church","submitted_at":"2012-10-05T20:01:29Z","abstract_excerpt":"FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S_n-representations. In this paper we prove the Noetherian property for FI-modules over arbitrary Noetherian rings: any sub-FI-module of a finitely generated FI-module is finitely generated. This lets us extend many of the results of [CEF] to representations in positive characteristic, and even to integral coefficients. We focus on three ma"},"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":"1210.1854","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-05T20:01:29Z","cross_cats_sorted":["math.AT","math.CO","math.GT"],"title_canon_sha256":"85ae73742689f11764a54bc300996f47047e3184b1afc911b37b87214e1fada5","abstract_canon_sha256":"cd6856cb800dc65a3351c1abb6b33383fa8f664049e738ba0f519d54ae43388e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:12.300858Z","signature_b64":"m05pMSdx7gU86cb86HeLAfMql6RcFA361KBOmPul77nzJpPfiR4NwPHzx7Z7V3ZXtuz1XRVdV6EpZFBIyIlzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7af01cd0db3b1ac58deeb776bf9a07983f5a1f7ce4e2f30cf651101b58ad51e4","last_reissued_at":"2026-05-18T02:31:12.300249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:12.300249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"FI-modules over Noetherian rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO","math.GT"],"primary_cat":"math.RT","authors_text":"Benson Farb, Jordan S. Ellenberg, Rohit Nagpal, Thomas Church","submitted_at":"2012-10-05T20:01:29Z","abstract_excerpt":"FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S_n-representations. In this paper we prove the Noetherian property for FI-modules over arbitrary Noetherian rings: any sub-FI-module of a finitely generated FI-module is finitely generated. This lets us extend many of the results of [CEF] to representations in positive characteristic, and even to integral coefficients. We focus on three ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1854","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":"1210.1854","created_at":"2026-05-18T02:31:12.300377+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.1854v2","created_at":"2026-05-18T02:31:12.300377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1854","created_at":"2026-05-18T02:31:12.300377+00:00"},{"alias_kind":"pith_short_12","alias_value":"PLYBZUG3HMNM","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PLYBZUG3HMNMLDPO","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PLYBZUG3","created_at":"2026-05-18T12:27:18.751474+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/PLYBZUG3HMNMLDPOW53L7GQHTA","json":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA.json","graph_json":"https://pith.science/api/pith-number/PLYBZUG3HMNMLDPOW53L7GQHTA/graph.json","events_json":"https://pith.science/api/pith-number/PLYBZUG3HMNMLDPOW53L7GQHTA/events.json","paper":"https://pith.science/paper/PLYBZUG3"},"agent_actions":{"view_html":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA","download_json":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA.json","view_paper":"https://pith.science/paper/PLYBZUG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.1854&json=true","fetch_graph":"https://pith.science/api/pith-number/PLYBZUG3HMNMLDPOW53L7GQHTA/graph.json","fetch_events":"https://pith.science/api/pith-number/PLYBZUG3HMNMLDPOW53L7GQHTA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA/action/storage_attestation","attest_author":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA/action/author_attestation","sign_citation":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA/action/citation_signature","submit_replication":"https://pith.science/pith/PLYBZUG3HMNMLDPOW53L7GQHTA/action/replication_record"}},"created_at":"2026-05-18T02:31:12.300377+00:00","updated_at":"2026-05-18T02:31:12.300377+00:00"}