{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VARIBMTLIAWD7MDZUVK5ST7EUZ","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":"ec6bd1c589c0c5263ff52f70a628e1a58c6033dc3fe43b39e462c341042de48f","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-27T12:47:09Z","title_canon_sha256":"ace2974bca97c7255364b89c96b7caa7e9936e283f3910bf382f6bd676d84999"},"schema_version":"1.0","source":{"id":"1109.5863","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5863","created_at":"2026-05-18T04:11:20Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5863v2","created_at":"2026-05-18T04:11:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5863","created_at":"2026-05-18T04:11:20Z"},{"alias_kind":"pith_short_12","alias_value":"VARIBMTLIAWD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VARIBMTLIAWD7MDZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VARIBMTL","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:934e7e3a35f562691c8384560e741ea87483842744a5cdba25d07217d0ab4aba","target":"graph","created_at":"2026-05-18T04:11:20Z","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"},"paper":{"abstract_excerpt":"Let $\\Gamma$ be a countable group acting on a countable set $X$ by permutations. We give a necessary and sufficient condition for the action to have a quasi-invariant mean with a given cocycle. This can be viewed as a combinatorial analogue of the condition for the existence of a quasi-invariant measure in the Borel case given by Miller. Then we show a geometric condition that guarantees that the corresponding action on the Stone-\\v{C}ech compactification is Zimmer amenable. The geometric condition (weighted hyperfiniteness) resembles Property A. We do not know the exact relation between the t","authors_text":"Adam Timar, Gabor Elek","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-27T12:47:09Z","title":"Quasi-invariant means and Zimmer amenability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5863","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:b15b8f503353824bc02aae525bce01f10a603bd9cb81ea6ecf989bf4bffef4e8","target":"record","created_at":"2026-05-18T04:11:20Z","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":"ec6bd1c589c0c5263ff52f70a628e1a58c6033dc3fe43b39e462c341042de48f","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-27T12:47:09Z","title_canon_sha256":"ace2974bca97c7255364b89c96b7caa7e9936e283f3910bf382f6bd676d84999"},"schema_version":"1.0","source":{"id":"1109.5863","kind":"arxiv","version":2}},"canonical_sha256":"a82280b26b402c3fb079a555d94fe4a6544ae4e27739f0f212a054a83b444904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a82280b26b402c3fb079a555d94fe4a6544ae4e27739f0f212a054a83b444904","first_computed_at":"2026-05-18T04:11:20.039162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:20.039162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CZLSCLOsB0eYn4BAtICjYr02fU2AEzchpEo2rbb1OiOzP+8vMe8lRmRCjEuYHTtQVke7S6kVbOzdIch9ubpmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:20.039639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5863","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b15b8f503353824bc02aae525bce01f10a603bd9cb81ea6ecf989bf4bffef4e8","sha256:934e7e3a35f562691c8384560e741ea87483842744a5cdba25d07217d0ab4aba"],"state_sha256":"c337ac27930204014d2c89f5373bf67cd509e027d05425f26f01fa1c32cefb41"}