{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VAEUQV3BA4M753DQN7DDQ2ZMQT","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":"76db2a2a429bde38b94eb24deb3c17246ea4bdad322f1433e7cb9b2e41d7c286","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-05T13:27:43Z","title_canon_sha256":"715e4884e45ebb72f0c23a017b079c1e000926e433b3680a868851f2e511383e"},"schema_version":"1.0","source":{"id":"2607.04300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04300","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04300v1","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04300","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"VAEUQV3BA4M7","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"VAEUQV3BA4M753DQ","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"VAEUQV3B","created_at":"2026-07-07T02:19:07Z"}],"graph_snapshots":[{"event_id":"sha256:643ad04e57dff1a000fef7c5fb722849b00f0fd55456d8cdb8d8713aeebab2a2","target":"graph","created_at":"2026-07-07T02:19:07Z","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/2607.04300/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish stable rank one for the reduced group C$^*$-algebras of the C$^*$-simple topological full groups and dynamical alternating groups constructed by Kerr and Tucker-Drob. The proof relies on both type II$_1$ and type III phenomena, in the first case via the use of F{\\o}lner towers and in the second via Ozawa's recent results on selflessness as applied to direct products of free products.","authors_text":"David Kerr, Spyridon Petrakos","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-05T13:27:43Z","title":"Topological full groups and stable rank one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04300","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:dc5395a4da03b1bef08fcdc8e7991041c729185119d3b0cf38e4ac807243d483","target":"record","created_at":"2026-07-07T02:19:07Z","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":"76db2a2a429bde38b94eb24deb3c17246ea4bdad322f1433e7cb9b2e41d7c286","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-05T13:27:43Z","title_canon_sha256":"715e4884e45ebb72f0c23a017b079c1e000926e433b3680a868851f2e511383e"},"schema_version":"1.0","source":{"id":"2607.04300","kind":"arxiv","version":1}},"canonical_sha256":"a8094857610719feec706fc6386b2c84d30ac43032c66906d8d5ceb76732d736","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8094857610719feec706fc6386b2c84d30ac43032c66906d8d5ceb76732d736","first_computed_at":"2026-07-07T02:19:07.579689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:19:07.579689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VziovzjZpt78n+jyCXpDyx4qgpj1kWY5IcMfxGwlXxO1Krm5/EvnrQQFy7fAcbO0cUGhtSIdc0NE0Vsn9Y9SCw==","signature_status":"signed_v1","signed_at":"2026-07-07T02:19:07.580485Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc5395a4da03b1bef08fcdc8e7991041c729185119d3b0cf38e4ac807243d483","sha256:643ad04e57dff1a000fef7c5fb722849b00f0fd55456d8cdb8d8713aeebab2a2"],"state_sha256":"4265133d31fedbf2387c4a4280e3700a6f6b61641c0647e7c870f6cd448fd69b"}