{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:W6KBBLNEISPFBAULNRYQDR4UJJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ce03f85b20dcfd40fadbf06437e606f1f5fa92febdc6a9bc2ae35d1c23e13aa2","cross_cats_sorted":["math.KT","math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-16T11:30:18Z","title_canon_sha256":"c7b4e856e0d1550da0f6b13e451f37625f8b7e6f9ed8995d9b74c3e3a4d508d9"},"schema_version":"1.0","source":{"id":"2405.09998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.09998","created_at":"2026-07-05T08:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"2405.09998v1","created_at":"2026-07-05T08:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.09998","created_at":"2026-07-05T08:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"W6KBBLNEISPF","created_at":"2026-07-05T08:19:51Z"},{"alias_kind":"pith_short_16","alias_value":"W6KBBLNEISPFBAUL","created_at":"2026-07-05T08:19:51Z"},{"alias_kind":"pith_short_8","alias_value":"W6KBBLNE","created_at":"2026-07-05T08:19:51Z"}],"graph_snapshots":[{"event_id":"sha256:81f518df9c6191d56032da84a36f124199b237a398d8cd0d68df7b578e85bc96","target":"graph","created_at":"2026-07-05T08:19:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.09998/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $R$ be a unital ring satisfying the invariant basis number property, that every stably free $R$-module is free, and that the complex of partial bases of every finite rank free module is Cohen--Macaulay. This class of rings includes every ring of stable rank $1$ (e.g. any local, semi-local or Artinian ring), every Euclidean domain, and every Dedekind domain $\\mathcal{O}_S$ of arithmetic type where $|S| > 1$ and $S$ contains at least one non-complex place. Extending recent work of Galatius--Kupers--Randal-Williams and Kupers--Miller--Patzt, we prove that the sequence of general linear groups","authors_text":"Calista Bernard, Jeremy Miller, Robin J. Sroka","cross_cats":["math.KT","math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-16T11:30:18Z","title":"Partial bases and homological stability of $\\operatorname{GL}_{n}(R)$ revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.09998","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f181ef87a62163ff6170ba148b5fb6cadb9489f5cb505ae978929673a5e278f9","target":"record","created_at":"2026-07-05T08:19:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ce03f85b20dcfd40fadbf06437e606f1f5fa92febdc6a9bc2ae35d1c23e13aa2","cross_cats_sorted":["math.KT","math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-16T11:30:18Z","title_canon_sha256":"c7b4e856e0d1550da0f6b13e451f37625f8b7e6f9ed8995d9b74c3e3a4d508d9"},"schema_version":"1.0","source":{"id":"2405.09998","kind":"arxiv","version":1}},"canonical_sha256":"b79410ada4449e50828b6c7101c7944a7e88d3f9ebd74679ae0197e28fbe9ea5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b79410ada4449e50828b6c7101c7944a7e88d3f9ebd74679ae0197e28fbe9ea5","first_computed_at":"2026-07-05T08:19:51.618267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:19:51.618267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aCL4U8L5w/3pUALZi+aTmmCPwX95UMEACWzlWdBKSY59qNeFMDZfhpK7A1omUcLqKp1CIsYeUVeldHjVs8r5Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:19:51.618701Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.09998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f181ef87a62163ff6170ba148b5fb6cadb9489f5cb505ae978929673a5e278f9","sha256:81f518df9c6191d56032da84a36f124199b237a398d8cd0d68df7b578e85bc96"],"state_sha256":"cab25dc2fd3b5212341933115eba10e7f023770bc35de5283ddc26ba7755144c"}