{"paper":{"title":"Coamenability and strong ergodicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For coamenable inclusions of ergodic probability measure-preserving relations, strong ergodicity holds for one exactly when it holds for the other.","cross_cats":["math.GR","math.OA"],"primary_cat":"math.DS","authors_text":"Ben Hayes","submitted_at":"2026-05-18T14:05:54Z","abstract_excerpt":"Following methods of Bannon-Marrakchi-Ozawa, we show that for coamenable inclusion $\\mathcal{S}\\leq \\mathcal{R}$ of ergodic, probability measure-preserving relations, we have that $\\mathcal{R}$ is strongly ergodic if and only if $\\mathcal{S}$ is strongly ergodic. More general results are given when $\\mathcal{S}\\leq \\mathcal{R}$ is coamenable, $\\mathcal{R}$ is strongly ergodic, but we do not assume ergodicity of $\\mathcal{S}$. As a consequence, if $\\Lambda\\leq \\Gamma$ is a coamenable inclusion of groups, then any strongly ergodic $\\Gamma$ action has countably many ergodic components for the $\\L"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"for coamenable inclusion S≤R of ergodic, probability measure-preserving relations, we have that R is strongly ergodic if and only if S is strongly ergodic.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The inclusion S ≤ R is coamenable (following methods of Bannon-Marrakchi-Ozawa), with both relations ergodic and probability measure-preserving.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"For coamenable inclusions S ≤ R of ergodic pmp relations, R is strongly ergodic iff S is; extends to group actions with countably many strongly ergodic ergodic components.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For coamenable inclusions of ergodic probability measure-preserving relations, strong ergodicity holds for one exactly when it holds for the other.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"da63a575ce05a4354125c20024605c7ac1f4e913e3f2838a56c7097d3792ef3f"},"source":{"id":"2605.18433","kind":"arxiv","version":1},"verdict":{"id":"b62686f8-5e5f-427e-9f78-659b38cb2147","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:36:47.982702Z","strongest_claim":"for coamenable inclusion S≤R of ergodic, probability measure-preserving relations, we have that R is strongly ergodic if and only if S is strongly ergodic.","one_line_summary":"For coamenable inclusions S ≤ R of ergodic pmp relations, R is strongly ergodic iff S is; extends to group actions with countably many strongly ergodic ergodic components.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The inclusion S ≤ R is coamenable (following methods of Bannon-Marrakchi-Ozawa), with both relations ergodic and probability measure-preserving.","pith_extraction_headline":"For coamenable inclusions of ergodic probability measure-preserving relations, strong ergodicity holds for one exactly when it holds for the other."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18433/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:20.233918Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T23:49:49.181140Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:40:55.321820Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:27.570519Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T23:31:32.349778Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T23:21:58.802971Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.652400Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d3c1b940f990cc5f7795a68d349f5db9278a781812441f5cd09a994dbb42aca1"},"references":{"count":41,"sample":[{"doi":"","year":2023,"title":"M. 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