{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WDM3YCSKUZCSJRGZ7RT5Z3PNAU","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":"f13462e345735ba9e708b837f953f02eb1ef22e16ebc3c11335d83799904dd51","cross_cats_sorted":["math.DS","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-13T12:00:43Z","title_canon_sha256":"a735d9c9f4d71f6eebe8f94c217581602b002ec34c69ffb98ee5387f489de4f5"},"schema_version":"1.0","source":{"id":"2605.13406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13406","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13406v1","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13406","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"WDM3YCSKUZCS","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"WDM3YCSKUZCSJRGZ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"WDM3YCSK","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:013e576727c7b00ef1c0fc4b1834e348fd81c05267a13d9288a49defec0fa426","target":"graph","created_at":"2026-05-18T02:44:47Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We exhibit a finitely generated group G that is not in C, such that G is amenable if and only if Thompson's group F is amenable."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the smoothness of the conjugacy relation (existence of a Borel transversal) is the right notion for 'classifiable' actions and that the explicit construction of G satisfies all the claimed dynamical and group-theoretic properties without hidden assumptions on the actions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Introduces class C of groups with smooth conjugacy for minimal line actions, proves stability and inclusion of piecewise affine groups, and exhibits a finitely generated G not in C with amenability equivalent to Thompson's F."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A finitely generated group G lies outside class C but is amenable precisely when Thompson's group F is amenable."}],"snapshot_sha256":"dea27e1b2819624ca9eb25e204758986aeebdb061430d0fcc03a721d2a4ef171"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a5dd0d8f59c10650c024cdbdc42ed85c57d12678783a888fbdf71e45c867062b"},"paper":{"abstract_excerpt":"We motivate and study the class $\\mathcal{C}$ of countable groups $G$ such that the conjugacy relation between minimal actions of $G$ on $\\mathbb{R}$ by orientation-preserving homeomorphisms is smooth -- that is, admits a Borel transversal. No example of amenable group outside of $\\mathcal{C}$ is known. We show a number of stability properties of $\\mathcal{C}$ under group-theoretic operations and that $\\mathcal{C}$ contains all finitely generated groups of piecewise affine homeomorphisms of the interval. We exhibit a finitely generated group $G$ that is not in $\\mathcal{C}$, such that $G$ is a","authors_text":"Joaqu\\'in Brum, Mart\\'in Gilabert Vio, Nicol\\'as Matte Bon","cross_cats":["math.DS","math.LO"],"headline":"A finitely generated group G lies outside class C but is amenable precisely when Thompson's group F is amenable.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-13T12:00:43Z","title":"Groups with classifiable actions on the line"},"references":{"count":49,"internal_anchors":0,"resolved_work":49,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"V. A. Antonov, Modeling of processes of cyclic evolution type. S ynchronization by a random signal , Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya (1984), no. vyp. 2, pp. 67-","work_id":"f22b0f5b-97e3-487f-9138-1b14d38b01f2","year":1984},{"cited_arxiv_id":"","doi":"10.2307/2371787","is_internal_anchor":false,"ref_index":2,"title":"Richard Arens, Topologies for homeomorphism groups https://doi.org/10.2307/2371787, American Journal of Mathematics 68 (1946), pp. 593--610","work_id":"5132d3ca-4cfa-44a7-9ad8-4252c8655ce0","year":1946},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Arsenin, Sur les projections de certains ensembles mesurables B , Doklady Akademii Nauk SSSR 27 (1940), pp","work_id":"fee048a3-804f-4235-8045-d05fa94c7b5d","year":1940},{"cited_arxiv_id":"","doi":"10.4171/jca/49","is_internal_anchor":false,"ref_index":4,"title":"Brin, and Justin Tatch Moore, https://doi.org/10.4171/jca/49 Complexity among the finitely generated subgroups of T hompson's group , Journal of Combinatorial Algebra 5 (2021), no","work_id":"61d095fd-45b9-44a7-8c34-c82923bcd1c0","year":2021},{"cited_arxiv_id":"","doi":"10.1017/cbo9780511735264","is_internal_anchor":false,"ref_index":5,"title":"Kechris, https://doi.org/10.1017/CBO9780511735264 The descriptive set theory of P olish group actions , London Mathematical Society Lecture Note Series, vol","work_id":"7d149df0-2f14-4292-b0e1-782d178c8023","year":1996}],"snapshot_sha256":"46b9c2135f56c36216d9b960e4282d0f843c0a3c3aea7b3965d7f986d160fc58"},"source":{"id":"2605.13406","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T18:31:29.690395Z","id":"c82a778d-4d5b-4ef4-a155-603bc2c05954","model_set":{"reader":"grok-4.3"},"one_line_summary":"Introduces class C of groups with smooth conjugacy for minimal line actions, proves stability and inclusion of piecewise affine groups, and exhibits a finitely generated G not in C with amenability equivalent to Thompson's F.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A finitely generated group G lies outside class C but is amenable precisely when Thompson's group F is amenable.","strongest_claim":"We exhibit a finitely generated group G that is not in C, such that G is amenable if and only if Thompson's group F is amenable.","weakest_assumption":"That the smoothness of the conjugacy relation (existence of a Borel transversal) is the right notion for 'classifiable' actions and that the explicit construction of G satisfies all the claimed dynamical and group-theoretic properties without hidden assumptions on the actions."}},"verdict_id":"c82a778d-4d5b-4ef4-a155-603bc2c05954"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6f2bee4d800ac3ce82086213753d61790ce3808ab7d352310c60a35232d9b3b3","target":"record","created_at":"2026-05-18T02:44:47Z","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":"f13462e345735ba9e708b837f953f02eb1ef22e16ebc3c11335d83799904dd51","cross_cats_sorted":["math.DS","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-13T12:00:43Z","title_canon_sha256":"a735d9c9f4d71f6eebe8f94c217581602b002ec34c69ffb98ee5387f489de4f5"},"schema_version":"1.0","source":{"id":"2605.13406","kind":"arxiv","version":1}},"canonical_sha256":"b0d9bc0a4aa64524c4d9fc67dceded0519412f4a97e4f646514ece9aa9c85350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0d9bc0a4aa64524c4d9fc67dceded0519412f4a97e4f646514ece9aa9c85350","first_computed_at":"2026-05-18T02:44:47.511825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:47.511825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p0OeY4HeTdKjbUeHnj+khU3RpKyyTzYSAGujPNhVrYk9oHg8UFDtk1bfH46jO0gB5iwgcIDkuHAwr18qwU1lAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:47.512334Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f2bee4d800ac3ce82086213753d61790ce3808ab7d352310c60a35232d9b3b3","sha256:013e576727c7b00ef1c0fc4b1834e348fd81c05267a13d9288a49defec0fa426"],"state_sha256":"b15b3fb255bab626cee024cd9fbfa3d37db20b305cb72e85b33b4ffc2c0b2fcf"}