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American Mathematical Society, Providence, RI, 2008","work_id":"d538db82-d501-4fcf-a655-ae914ba7c826","year":2008}],"snapshot_sha256":"8021850f6d4ef8aa2a2a3da495970e706266d2c5b53c995a55e60634588de8b6"},"source":{"id":"2605.18433","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T23:36:47.982702Z","id":"b62686f8-5e5f-427e-9f78-659b38cb2147","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"For coamenable inclusions of ergodic probability measure-preserving relations, strong ergodicity holds for one exactly when it holds for the other.","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.","weakest_assumption":"The inclusion S ≤ R is coamenable (following methods of Bannon-Marrakchi-Ozawa), with both relations ergodic and probability measure-preserving."}},"verdict_id":"b62686f8-5e5f-427e-9f78-659b38cb2147"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bb8831c4c587f0e10d390647c43f15482e7ce2b2cfe8a53464bf0b010351c0b0","target":"record","created_at":"2026-05-20T00:06:00Z","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":"c0625a1d2dadd320d1878c7c99fb2c2942ac4b35b06f3dc0efb6e8d16e13edbb","cross_cats_sorted":["math.GR","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-18T14:05:54Z","title_canon_sha256":"c0e0382f3f73c319fb1424539520760053ce6e0ef828fe92dea69f5b90148557"},"schema_version":"1.0","source":{"id":"2605.18433","kind":"arxiv","version":1}},"canonical_sha256":"8477752db4b88b952b296e9d1361450a0085a5cc12e7b55b84fe5c80ad71585c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8477752db4b88b952b296e9d1361450a0085a5cc12e7b55b84fe5c80ad71585c","first_computed_at":"2026-05-20T00:06:00.700648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:06:00.700648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mtji4+2NRrsaWmX70ZPMz3lkmmMn1xsLp7H+sY/rV37kT2kz1+QYNDKc+/beN2XaLICz2Kbh+oSEm9cD3UVRBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:06:00.701718Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb8831c4c587f0e10d390647c43f15482e7ce2b2cfe8a53464bf0b010351c0b0","sha256:d02c3311b171c934600c6664906f766b62b03e3f7943aee95ad284af408445a5"],"state_sha256":"4c4c78fbb2616b727ccb25cbc740048c5d8aa51edba5842609fa3c0a27d4eb0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jW65rbhLtDzT8zkahaneQHxZ16aFR6BtDxOoWyeHjGXQHk40ppGaIPpJVKFM8AG8a1rXtpQUFs5XiLDClXPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:49:34.468461Z","bundle_sha256":"a99196b3a93fef9cf1491c1c3ad72df0e2a46c129420205ef61edbaca7f510fc"}}