{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:A5HMYKQAMEYLWARIMB2TN44PJH","short_pith_number":"pith:A5HMYKQA","schema_version":"1.0","canonical_sha256":"074ecc2a006130bb0228607536f38f49dbd3ad38abd30baf111e158c655e3bbf","source":{"kind":"arxiv","id":"1408.6692","version":1},"attestation_state":"computed","paper":{"title":"Ergodic Theorems for coset spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.DS","authors_text":"Alexander Fish, Michael Bj\\\"orklund","submitted_at":"2014-08-28T12:11:08Z","abstract_excerpt":"We study in this paper the validity of the mean ergodic theorem along \\emph{left} F\\o lner sequences in a countable amenable group $G$. Although the \\emph{weak} ergodic theorem always holds along \\emph{any} left F\\o lner sequence in $G$, we provide examples where the \\emph{mean} ergodic theorem fails in quite dramatic ways. On the other hand, if $G$ does not admit any ICC quotients, e.g. if $G$ is virtually nilpotent, then we prove that the mean ergodic theorem does indeed hold along \\emph{any} left F\\o lner sequence.\n  In the case when a unitary representation of a countable amenable group is"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.6692","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-28T12:11:08Z","cross_cats_sorted":["math.GR","math.PR"],"title_canon_sha256":"9cd13e0e54c5d6341563a046ef0262a0a9483de3b102dedf14fa34d504ab1c71","abstract_canon_sha256":"ed65e70220b2e2584dc1820268766945e595091d86809d0f56f9b3ab4b9b1f47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:01.040905Z","signature_b64":"pubutLD+oQhL2+6xDQ17W5/zOHKM9j6z+vDori8WRTGZTBqAW6zMrdy39X2DTgDcxNenxje36Bq09MNA3ilACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"074ecc2a006130bb0228607536f38f49dbd3ad38abd30baf111e158c655e3bbf","last_reissued_at":"2026-05-18T02:44:01.040422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:01.040422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic Theorems for coset spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.DS","authors_text":"Alexander Fish, Michael Bj\\\"orklund","submitted_at":"2014-08-28T12:11:08Z","abstract_excerpt":"We study in this paper the validity of the mean ergodic theorem along \\emph{left} F\\o lner sequences in a countable amenable group $G$. Although the \\emph{weak} ergodic theorem always holds along \\emph{any} left F\\o lner sequence in $G$, we provide examples where the \\emph{mean} ergodic theorem fails in quite dramatic ways. On the other hand, if $G$ does not admit any ICC quotients, e.g. if $G$ is virtually nilpotent, then we prove that the mean ergodic theorem does indeed hold along \\emph{any} left F\\o lner sequence.\n  In the case when a unitary representation of a countable amenable group is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6692","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.6692","created_at":"2026-05-18T02:44:01.040492+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.6692v1","created_at":"2026-05-18T02:44:01.040492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6692","created_at":"2026-05-18T02:44:01.040492+00:00"},{"alias_kind":"pith_short_12","alias_value":"A5HMYKQAMEYL","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"A5HMYKQAMEYLWARI","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"A5HMYKQA","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH","json":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH.json","graph_json":"https://pith.science/api/pith-number/A5HMYKQAMEYLWARIMB2TN44PJH/graph.json","events_json":"https://pith.science/api/pith-number/A5HMYKQAMEYLWARIMB2TN44PJH/events.json","paper":"https://pith.science/paper/A5HMYKQA"},"agent_actions":{"view_html":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH","download_json":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH.json","view_paper":"https://pith.science/paper/A5HMYKQA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.6692&json=true","fetch_graph":"https://pith.science/api/pith-number/A5HMYKQAMEYLWARIMB2TN44PJH/graph.json","fetch_events":"https://pith.science/api/pith-number/A5HMYKQAMEYLWARIMB2TN44PJH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH/action/storage_attestation","attest_author":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH/action/author_attestation","sign_citation":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH/action/citation_signature","submit_replication":"https://pith.science/pith/A5HMYKQAMEYLWARIMB2TN44PJH/action/replication_record"}},"created_at":"2026-05-18T02:44:01.040492+00:00","updated_at":"2026-05-18T02:44:01.040492+00:00"}