{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RRFJK76DTDZO4B5JM5MZUT43PU","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":"b61bba343ba8b6a0c5b97db2aedff880176792eb4da35fa44295555d4cd5e683","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-14T02:19:21Z","title_canon_sha256":"e496b373408070c796c2b70708bee37ec3b82ee2288f46b6b14e5d968badd58b"},"schema_version":"1.0","source":{"id":"2501.07791","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.07791","created_at":"2026-07-05T10:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"2501.07791v2","created_at":"2026-07-05T10:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.07791","created_at":"2026-07-05T10:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"RRFJK76DTDZO","created_at":"2026-07-05T10:17:52Z"},{"alias_kind":"pith_short_16","alias_value":"RRFJK76DTDZO4B5J","created_at":"2026-07-05T10:17:52Z"},{"alias_kind":"pith_short_8","alias_value":"RRFJK76D","created_at":"2026-07-05T10:17:52Z"}],"graph_snapshots":[{"event_id":"sha256:aa3f49965fc1b5ea5149d20f0ee08fd875f5533efafecfe96de9f87a7b0eb672","target":"graph","created_at":"2026-07-05T10:17:52Z","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/2501.07791/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct the first examples of residually finite amenable groups that are not Hilbert-Schmidt (HS) stable. We construct finitely generated, class 3 nilpotent by cyclic examples and solvable linear finitely presented examples. This also provides the first examples of amenable groups that are very flexibly HS-stable but not flexibly HS-stable and the first examples of residually finite amenable groups that are not locally HS-stable. Along the way we exhibit (necessarily not-finitely-generated) class 2 nilpotent groups $G = A\\rtimes \\Z$ with $A$ abelian such that the periodic points of the du","authors_text":"Caleb Eckhardt","cross_cats":["math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-14T02:19:21Z","title":"Residually finite amenable groups that are not Hilbert-Schmidt stable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07791","kind":"arxiv","version":2},"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":"sha256:99b239b73b8c8e10608d4c33af502967216fa8d99eb4a966acf99d02b638e018","target":"record","created_at":"2026-07-05T10:17:52Z","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":"b61bba343ba8b6a0c5b97db2aedff880176792eb4da35fa44295555d4cd5e683","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-14T02:19:21Z","title_canon_sha256":"e496b373408070c796c2b70708bee37ec3b82ee2288f46b6b14e5d968badd58b"},"schema_version":"1.0","source":{"id":"2501.07791","kind":"arxiv","version":2}},"canonical_sha256":"8c4a957fc398f2ee07a967599a4f9b7d08cf7930ab11e38e93b0041e30558d61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c4a957fc398f2ee07a967599a4f9b7d08cf7930ab11e38e93b0041e30558d61","first_computed_at":"2026-07-05T10:17:52.965683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:17:52.965683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xJIXe+nJIzod39jVBWdgtbgGtyU2Pz9dqGHr7HXllGnAu36KN85h/Bb0He9Je0I5so5FD3CE31mkQNck8cXHAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:17:52.966167Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.07791","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99b239b73b8c8e10608d4c33af502967216fa8d99eb4a966acf99d02b638e018","sha256:aa3f49965fc1b5ea5149d20f0ee08fd875f5533efafecfe96de9f87a7b0eb672"],"state_sha256":"4d1284a669b9836159a8795f3972fd02db629b37cf9037fe6ac468368cc9a701"}