{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DSYTANO66QIHZC3JBDBVGRPOHP","short_pith_number":"pith:DSYTANO6","schema_version":"1.0","canonical_sha256":"1cb13035def4107c8b6908c35345ee3bfb31ee6afabefcd16c6c7cda0c94a016","source":{"kind":"arxiv","id":"1610.07351","version":2},"attestation_state":"computed","paper":{"title":"Fibred cofinitely-coarse embeddability of box families and proper isometric affine actions on uniformly convex Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Guoqiang Li, Xianjin Wang","submitted_at":"2016-10-24T10:43:57Z","abstract_excerpt":"In this paper we show that a countable, residually amenable group admits a proper isometric affine action on some uniformly convex Banach space if and only if one (or equivalently, all) of its box families admits a fibred cofinitely-coarse embedding into some uniformly convex Banach space."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.07351","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-24T10:43:57Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"9448ea5a783042cbd64eab1d224832b6510dfb8ea05830f5e3f497819c09340a","abstract_canon_sha256":"9ddff568622b05b2695ac27be3645b94303eaeb5055f7f34683515c87d32d487"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:56.094783Z","signature_b64":"amlsWYbjHzmfWBXiO+ngRdkxhLIsABUtyMShxhLziDN+XeRc48G3plPuR2tOYwH6kQCFoEqOM4/wrzJGxpYpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb13035def4107c8b6908c35345ee3bfb31ee6afabefcd16c6c7cda0c94a016","last_reissued_at":"2026-05-18T00:31:56.094319Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:56.094319Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibred cofinitely-coarse embeddability of box families and proper isometric affine actions on uniformly convex Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Guoqiang Li, Xianjin Wang","submitted_at":"2016-10-24T10:43:57Z","abstract_excerpt":"In this paper we show that a countable, residually amenable group admits a proper isometric affine action on some uniformly convex Banach space if and only if one (or equivalently, all) of its box families admits a fibred cofinitely-coarse embedding into some uniformly convex Banach space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07351","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.07351","created_at":"2026-05-18T00:31:56.094379+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07351v2","created_at":"2026-05-18T00:31:56.094379+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07351","created_at":"2026-05-18T00:31:56.094379+00:00"},{"alias_kind":"pith_short_12","alias_value":"DSYTANO66QIH","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DSYTANO66QIHZC3J","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DSYTANO6","created_at":"2026-05-18T12:30:12.583610+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP","json":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP.json","graph_json":"https://pith.science/api/pith-number/DSYTANO66QIHZC3JBDBVGRPOHP/graph.json","events_json":"https://pith.science/api/pith-number/DSYTANO66QIHZC3JBDBVGRPOHP/events.json","paper":"https://pith.science/paper/DSYTANO6"},"agent_actions":{"view_html":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP","download_json":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP.json","view_paper":"https://pith.science/paper/DSYTANO6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07351&json=true","fetch_graph":"https://pith.science/api/pith-number/DSYTANO66QIHZC3JBDBVGRPOHP/graph.json","fetch_events":"https://pith.science/api/pith-number/DSYTANO66QIHZC3JBDBVGRPOHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP/action/storage_attestation","attest_author":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP/action/author_attestation","sign_citation":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP/action/citation_signature","submit_replication":"https://pith.science/pith/DSYTANO66QIHZC3JBDBVGRPOHP/action/replication_record"}},"created_at":"2026-05-18T00:31:56.094379+00:00","updated_at":"2026-05-18T00:31:56.094379+00:00"}