{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H4MAVVF2UGLXDZIXX3A3HPVZ4R","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":"eb9b07569f91781a755c55c41bbc89122b074a6d8c456186bb4d21f337925a33","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-04T09:30:02Z","title_canon_sha256":"5294bd35ff207bd62bd19b0e59ba27b47f5126d2d77a354493ed0415d08f7bcd"},"schema_version":"1.0","source":{"id":"1605.01192","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01192","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01192v3","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01192","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"pith_short_12","alias_value":"H4MAVVF2UGLX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H4MAVVF2UGLXDZIX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H4MAVVF2","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:2e8f5215897dc67702a43ddb48bc16cc550305ff3e1f8aa7d659db19eaacfb0b","target":"graph","created_at":"2026-05-18T00:33:53Z","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 a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.","authors_text":"Goulnara Arzhantseva, Romain Tessera","cross_cats":["math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-04T09:30:02Z","title":"Admitting a coarse embedding is not preserved under group extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01192","kind":"arxiv","version":3},"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":"sha256:5474beb53e68874b58dc737adfeeb786bba47484c20522577ef6fb8f1be63a3d","target":"record","created_at":"2026-05-18T00:33:53Z","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":"eb9b07569f91781a755c55c41bbc89122b074a6d8c456186bb4d21f337925a33","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-04T09:30:02Z","title_canon_sha256":"5294bd35ff207bd62bd19b0e59ba27b47f5126d2d77a354493ed0415d08f7bcd"},"schema_version":"1.0","source":{"id":"1605.01192","kind":"arxiv","version":3}},"canonical_sha256":"3f180ad4baa19771e517bec1b3beb9e4715da7a1303bbb3f292ee3428f5231d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f180ad4baa19771e517bec1b3beb9e4715da7a1303bbb3f292ee3428f5231d1","first_computed_at":"2026-05-18T00:33:53.331913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:53.331913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zbSxWwdMtfjAA0a7veKmDPjM27lpUQF69IqHy2E4fh0M5qSWn6YJGqskrOsahpTBFAPsueA4XpMdmAnYDlpjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:53.332429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01192","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5474beb53e68874b58dc737adfeeb786bba47484c20522577ef6fb8f1be63a3d","sha256:2e8f5215897dc67702a43ddb48bc16cc550305ff3e1f8aa7d659db19eaacfb0b"],"state_sha256":"bea65767e03981616cd98d85cbb5265a79952802a9907b1976a6680da42e8edd"}