{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U5K2LDHLWYAFUL2JBUQHXL5C6P","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":"530ec7f4afe868b53e93d6c08f26fb53ac37f04385ea364a3617bbee0a69b73c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-11T14:26:31Z","title_canon_sha256":"6fca12248a34e17bb4670d2d612c572d694ff288c79e68a3e3ab9bc48948906f"},"schema_version":"1.0","source":{"id":"1307.3122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3122","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3122v1","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3122","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"U5K2LDHLWYAF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U5K2LDHLWYAFUL2J","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U5K2LDHL","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:2cd091ad48e551f69a0146dd3ab50ec29fc006db157d8a50c5a742f5d8435168","target":"graph","created_at":"2026-05-18T03:18:41Z","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":"Given two finitely generated groups that coarsely embed into a Hilbert space, it is known that their wreath product also embeds coarsely into a Hilbert space. We introduce a wreath product construction for general metric spaces X,Y,Z and derive a condition, called the (delta-polynomial) path lifting property, such that coarse embeddability of X,Y and Z implies coarse embeddability of X\\wr_Z Y. We also give bounds on the compression of X\\wr_Z Y in terms of delta and the compressions of X,Y and Z. Next, we investigate the stability of the property of admitting a box space which coarsely embeds i","authors_text":"Ana Khukhro, Chris Cave, Dennis Dreesen","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-11T14:26:31Z","title":"Embeddability of generalized wreath products and box spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3122","kind":"arxiv","version":1},"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:f9330c6e8067f51a8c06c40abe7c3e956b0a68587eef80f17baadf9aa609a545","target":"record","created_at":"2026-05-18T03:18:41Z","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":"530ec7f4afe868b53e93d6c08f26fb53ac37f04385ea364a3617bbee0a69b73c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-11T14:26:31Z","title_canon_sha256":"6fca12248a34e17bb4670d2d612c572d694ff288c79e68a3e3ab9bc48948906f"},"schema_version":"1.0","source":{"id":"1307.3122","kind":"arxiv","version":1}},"canonical_sha256":"a755a58cebb6005a2f490d207bafa2f3f1fd5aca0cd0a9007e0ebfabe0babdd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a755a58cebb6005a2f490d207bafa2f3f1fd5aca0cd0a9007e0ebfabe0babdd6","first_computed_at":"2026-05-18T03:18:41.126985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:41.126985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F1i1g9uuBJjVUai0vqqMWjaPk4NoJnJQoBHChoWdM1e6YJH7z/t2DohQ25Xzui6t5K4X1m5T9O/6RT2oD5VLBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:41.128197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9330c6e8067f51a8c06c40abe7c3e956b0a68587eef80f17baadf9aa609a545","sha256:2cd091ad48e551f69a0146dd3ab50ec29fc006db157d8a50c5a742f5d8435168"],"state_sha256":"8a78169948fa34ef0247215b3b3761dfc5c4008ba1ba542e586d4a128211bcc0"}