{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OUHI6BPBFKQR5FNUAR57XB7KBN","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":"0b8ff3db6cea39a445f4e8852d400b32c98783240b3feef3638b87c49849073c","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-26T19:02:01Z","title_canon_sha256":"19597fc59be4c1e61fb08484175d674ff826fc0436b824a55163befa0f2201ee"},"schema_version":"1.0","source":{"id":"1002.5040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.5040","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1002.5040v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.5040","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"OUHI6BPBFKQR","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OUHI6BPBFKQR5FNU","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OUHI6BPB","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:910f4f7b85cae328d6ab08659b827341ffa6f9713e7a4eaa23a1026df691b323","target":"graph","created_at":"2026-05-18T02:38:18Z","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":"Property A was introduced by Yu as a non-equivariant analogue of amenability. Nigel Higson posed the question of whether there is a homological characterisation of property A. In this paper we answer Higson's question affirmatively by constructing analogues of group cohomology and bounded cohomology for a metric space X, and show that property A is equivalent to vanishing cohomology. Using these cohomology theories we also give a characterisation of property A in terms of the existence of an asymptotically invariant mean on the space.","authors_text":"G. A. Niblo, J. Brodzki, N. J. Wright","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-26T19:02:01Z","title":"A cohomological characterisation of Yu's Property A for metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.5040","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:cc54979ac4d16ee0ed58b9492503f6943340135b4caf34e9c523ab781cb47a7b","target":"record","created_at":"2026-05-18T02:38:18Z","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":"0b8ff3db6cea39a445f4e8852d400b32c98783240b3feef3638b87c49849073c","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-26T19:02:01Z","title_canon_sha256":"19597fc59be4c1e61fb08484175d674ff826fc0436b824a55163befa0f2201ee"},"schema_version":"1.0","source":{"id":"1002.5040","kind":"arxiv","version":2}},"canonical_sha256":"750e8f05e12aa11e95b4047bfb87ea0b72b68a8ddb23b7010df2806205d21e7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"750e8f05e12aa11e95b4047bfb87ea0b72b68a8ddb23b7010df2806205d21e7e","first_computed_at":"2026-05-18T02:38:18.592452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.592452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4xcL7IvsmknyRJfo4GWBzBOM/VWeSCcWBXF6VBocMutPewjLHt1zOcUndL4MbN2v9dJWHDhT9RfYGpz9dplAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.593023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.5040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc54979ac4d16ee0ed58b9492503f6943340135b4caf34e9c523ab781cb47a7b","sha256:910f4f7b85cae328d6ab08659b827341ffa6f9713e7a4eaa23a1026df691b323"],"state_sha256":"a932899aa18ebcfd61802a349a4240f8f162fe95fb1d60196cd41692da2ddbf4"}