{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EBGV2TFYE2HHEY2JIVQWOKEYV5","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":"2b1dd019cbfdcbe356d404075dbf9eabdab8d16a8830f22da5cc4a0044dcfbd9","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-15T00:43:03Z","title_canon_sha256":"4a48c8228c698920309c9da12df55f68076508015830c63a0ef0dd0f396eba2e"},"schema_version":"1.0","source":{"id":"2512.12894","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.12894","created_at":"2026-05-20T00:02:08Z"},{"alias_kind":"arxiv_version","alias_value":"2512.12894v2","created_at":"2026-05-20T00:02:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.12894","created_at":"2026-05-20T00:02:08Z"},{"alias_kind":"pith_short_12","alias_value":"EBGV2TFYE2HH","created_at":"2026-05-20T00:02:08Z"},{"alias_kind":"pith_short_16","alias_value":"EBGV2TFYE2HHEY2J","created_at":"2026-05-20T00:02:08Z"},{"alias_kind":"pith_short_8","alias_value":"EBGV2TFY","created_at":"2026-05-20T00:02:08Z"}],"graph_snapshots":[{"event_id":"sha256:08e02953fa0dd1852478d9641098d2199a0008627f79efa2b6a40c11dee3e978","target":"graph","created_at":"2026-05-20T00:02:08Z","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/2512.12894/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we show that the ergodic averages of the action of any unimodular amenable group along certain F{\\o}lner sequences can be dominated by the Ces\\`aro means of a suitably constructed Markov operator, that is, the ergodic averages of an integer action. Moreover, the restriction on these F{\\o}lner sequences are mild enough so that every two-sided F{\\o}lner sequence has a subsequence satisfying these conditions. As a consequence of this inequality, we obtain the maximal and pointwise (individual) ergodic theorems for actions of unimodular amenable groups directly from the corresponding","authors_text":"Joachim Zacharias, Runlian Xia, Ujan Chakraborty","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-15T00:43:03Z","title":"Ergodic Average Dominance for Unimodular Amenable Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.12894","kind":"arxiv","version":2},"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":"sha256:8303840f2fdb2736c359fd8a8bac8f14b84d76494a4df81cb431e29b2b85858d","target":"record","created_at":"2026-05-20T00:02:08Z","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":"2b1dd019cbfdcbe356d404075dbf9eabdab8d16a8830f22da5cc4a0044dcfbd9","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-15T00:43:03Z","title_canon_sha256":"4a48c8228c698920309c9da12df55f68076508015830c63a0ef0dd0f396eba2e"},"schema_version":"1.0","source":{"id":"2512.12894","kind":"arxiv","version":2}},"canonical_sha256":"204d5d4cb8268e7263494561672898af5e5ded4862a65ca00aaf6f7dad8756d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"204d5d4cb8268e7263494561672898af5e5ded4862a65ca00aaf6f7dad8756d0","first_computed_at":"2026-05-20T00:02:08.019436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:08.019436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7zwE9lq2STjaPKHUFo2t2aTulC9qRbG+c4G1vqaZ6fIneB+3NkxAkV+/FH1/uy09F9O4VVL+ogco2CUGfEvWDg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:08.020277Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.12894","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8303840f2fdb2736c359fd8a8bac8f14b84d76494a4df81cb431e29b2b85858d","sha256:08e02953fa0dd1852478d9641098d2199a0008627f79efa2b6a40c11dee3e978"],"state_sha256":"de6cf82560e71730ef31575198aa8dcb47c9bffaf6d8405bac0554fd3367b1ff"}