{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TVQFQNPKVVGRXOGEK3N4ZKPYCL","short_pith_number":"pith:TVQFQNPK","schema_version":"1.0","canonical_sha256":"9d605835eaad4d1bb8c456dbcca9f812ca9bf44e87262c81b185c3dcb94374bb","source":{"kind":"arxiv","id":"1711.11080","version":4},"attestation_state":"computed","paper":{"title":"Stability in the homology of unipotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.AT","authors_text":"Andrew Putman, Andrew Snowden, Steven V Sam","submitted_at":"2017-11-29T19:55:59Z","abstract_excerpt":"Let $R$ be a (not necessarily commutative) ring whose additive group is finitely generated and let $U_n(R) \\subset GL_n(R)$ be the group of upper-triangular unipotent matrices over $R$. We study how the homology groups of $U_n(R)$ vary with $n$ from the point of view of representation stability. Our main theorem asserts that if for each $n$ we have representations $M_n$ of $U_n(R)$ over a ring $\\mathbf{k}$ that are appropriately compatible and satisfy suitable finiteness hypotheses, then the rule $[n] \\mapsto \\widetilde{H}_i(U_n(R),M_n)$ defines a finitely generated OI-module. As a consequence"},"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":"1711.11080","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-29T19:55:59Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"bb829ac76e23389dec5abca84ee88d0821689b22d1da9d5aa42f4767a6c40355","abstract_canon_sha256":"2b94ca83a8803240106170e196e9f5486f4b1a4327630ff9f0af6e7534e5efa9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:35.929205Z","signature_b64":"DizUCdogOxAwkfLRoYztT9AEjAaup3/d+UhSiaSzC/91uB7b/Gd8knLi1nAB5LWyX5qYB2/FV6he16gGH+YnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d605835eaad4d1bb8c456dbcca9f812ca9bf44e87262c81b185c3dcb94374bb","last_reissued_at":"2026-07-05T00:48:35.928826Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:35.928826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability in the homology of unipotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.AT","authors_text":"Andrew Putman, Andrew Snowden, Steven V Sam","submitted_at":"2017-11-29T19:55:59Z","abstract_excerpt":"Let $R$ be a (not necessarily commutative) ring whose additive group is finitely generated and let $U_n(R) \\subset GL_n(R)$ be the group of upper-triangular unipotent matrices over $R$. We study how the homology groups of $U_n(R)$ vary with $n$ from the point of view of representation stability. Our main theorem asserts that if for each $n$ we have representations $M_n$ of $U_n(R)$ over a ring $\\mathbf{k}$ that are appropriately compatible and satisfy suitable finiteness hypotheses, then the rule $[n] \\mapsto \\widetilde{H}_i(U_n(R),M_n)$ defines a finitely generated OI-module. As a consequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11080","kind":"arxiv","version":4},"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/1711.11080/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":"1711.11080","created_at":"2026-07-05T00:48:35.928883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.11080v4","created_at":"2026-07-05T00:48:35.928883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11080","created_at":"2026-07-05T00:48:35.928883+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVQFQNPKVVGR","created_at":"2026-07-05T00:48:35.928883+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVQFQNPKVVGRXOGE","created_at":"2026-07-05T00:48:35.928883+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVQFQNPK","created_at":"2026-07-05T00:48:35.928883+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/TVQFQNPKVVGRXOGEK3N4ZKPYCL","json":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL.json","graph_json":"https://pith.science/api/pith-number/TVQFQNPKVVGRXOGEK3N4ZKPYCL/graph.json","events_json":"https://pith.science/api/pith-number/TVQFQNPKVVGRXOGEK3N4ZKPYCL/events.json","paper":"https://pith.science/paper/TVQFQNPK"},"agent_actions":{"view_html":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL","download_json":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL.json","view_paper":"https://pith.science/paper/TVQFQNPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.11080&json=true","fetch_graph":"https://pith.science/api/pith-number/TVQFQNPKVVGRXOGEK3N4ZKPYCL/graph.json","fetch_events":"https://pith.science/api/pith-number/TVQFQNPKVVGRXOGEK3N4ZKPYCL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/action/storage_attestation","attest_author":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/action/author_attestation","sign_citation":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/action/citation_signature","submit_replication":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/action/replication_record"}},"created_at":"2026-07-05T00:48:35.928883+00:00","updated_at":"2026-07-05T00:48:35.928883+00:00"}