{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z2Q37II2GH4IOVAGHH4ZF2EPFR","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":"4fd9d7e70fb7612775bc77a84877126d749393e527e3ac30934226e5c9627561","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-10T23:58:44Z","title_canon_sha256":"cbc9043b7b25559ff85c300a93f744926c2775d7b80b7fec4bd8cf40505f6084"},"schema_version":"1.0","source":{"id":"1101.1993","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1993","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1993v2","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1993","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z2Q37II2GH4I","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z2Q37II2GH4IOVAG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z2Q37II2","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:75c2f6221bd07b6871bc0773e82af42e0c96f8fe4cf3a5ae995086c274083121","target":"graph","created_at":"2026-05-18T04:09:53Z","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":"We construct the first example of a coarsely non-amenable (= without Guoliang Yu's property A) metric space with bounded geometry which coarsely embeds into a Hilbert space.","authors_text":"Erik Guentner, Goulnara Arzhantseva, Jan Spakula","cross_cats":["math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-10T23:58:44Z","title":"Coarse non-amenability and coarse embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1993","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":"sha256:6302762c5b7b2c1b14c2c0974a0b7632cc0c854c86febd125f17d7795b24575a","target":"record","created_at":"2026-05-18T04:09:53Z","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":"4fd9d7e70fb7612775bc77a84877126d749393e527e3ac30934226e5c9627561","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-10T23:58:44Z","title_canon_sha256":"cbc9043b7b25559ff85c300a93f744926c2775d7b80b7fec4bd8cf40505f6084"},"schema_version":"1.0","source":{"id":"1101.1993","kind":"arxiv","version":2}},"canonical_sha256":"cea1bfa11a31f887540639f992e88f2c5776078dcf3e246a3f29ef96e5771522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea1bfa11a31f887540639f992e88f2c5776078dcf3e246a3f29ef96e5771522","first_computed_at":"2026-05-18T04:09:53.708828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:53.708828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"azcZu1qrZ45/M0rLXH2c7oIv+QKAI38zAK+qZbCdeoHudkUOgKvlHrXI33QSJQzlG4DBLsZhja2HcajWPNi9Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:53.709498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1993","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6302762c5b7b2c1b14c2c0974a0b7632cc0c854c86febd125f17d7795b24575a","sha256:75c2f6221bd07b6871bc0773e82af42e0c96f8fe4cf3a5ae995086c274083121"],"state_sha256":"e5cb537c0b8e247974c9e2817c0f3baf6a494f46201a98d643d737dfe6e49557"}