{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:435ZDOSXG4UVUAGYKL7YGEDH6Y","short_pith_number":"pith:435ZDOSX","schema_version":"1.0","canonical_sha256":"e6fb91ba5737295a00d852ff831067f60aeb9f40890c65cd7ff22d2a8daf2e7d","source":{"kind":"arxiv","id":"1710.03085","version":2},"attestation_state":"computed","paper":{"title":"Rigidity of warped cones and coarse geometry of expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.GT"],"primary_cat":"math.MG","authors_text":"David Fisher, Thang Nguyen, Wouter van Limbeek","submitted_at":"2017-10-09T13:44:24Z","abstract_excerpt":"We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian factors, then two such warped cones are quasi-isometric if and only if the actions are finite covers of conjugate actions. As a consequence, we produce continuous families of non-quasi-isometric expanders and superexpanders. The proof relies on the use of coarse topology for warped cones, such as a computation of their coarse fundamental groups."},"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":"1710.03085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-10-09T13:44:24Z","cross_cats_sorted":["math.CO","math.GR","math.GT"],"title_canon_sha256":"08d8f3efdf45df0704bb3e929b58df980bfbbfb61348d3d078387ed2276cfbb0","abstract_canon_sha256":"e5e7acc1ba756e4c3c01b82e66f64c9a7da1eb8720c191aea50c6b7d115583b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:36.337653Z","signature_b64":"tBLywTLYF0P+7+198jCv/ZWW1ExHTd1y6UH5Eo+006Hx3oTCApBHXfy0CR455wGqSwdSRfPx8KailF5ggRlMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6fb91ba5737295a00d852ff831067f60aeb9f40890c65cd7ff22d2a8daf2e7d","last_reissued_at":"2026-05-18T00:26:36.337145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:36.337145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of warped cones and coarse geometry of expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.GT"],"primary_cat":"math.MG","authors_text":"David Fisher, Thang Nguyen, Wouter van Limbeek","submitted_at":"2017-10-09T13:44:24Z","abstract_excerpt":"We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian factors, then two such warped cones are quasi-isometric if and only if the actions are finite covers of conjugate actions. As a consequence, we produce continuous families of non-quasi-isometric expanders and superexpanders. The proof relies on the use of coarse topology for warped cones, such as a computation of their coarse fundamental groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03085","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":"1710.03085","created_at":"2026-05-18T00:26:36.337216+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.03085v2","created_at":"2026-05-18T00:26:36.337216+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03085","created_at":"2026-05-18T00:26:36.337216+00:00"},{"alias_kind":"pith_short_12","alias_value":"435ZDOSXG4UV","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"435ZDOSXG4UVUAGY","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"435ZDOSX","created_at":"2026-05-18T12:30:58.224056+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/435ZDOSXG4UVUAGYKL7YGEDH6Y","json":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y.json","graph_json":"https://pith.science/api/pith-number/435ZDOSXG4UVUAGYKL7YGEDH6Y/graph.json","events_json":"https://pith.science/api/pith-number/435ZDOSXG4UVUAGYKL7YGEDH6Y/events.json","paper":"https://pith.science/paper/435ZDOSX"},"agent_actions":{"view_html":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y","download_json":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y.json","view_paper":"https://pith.science/paper/435ZDOSX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.03085&json=true","fetch_graph":"https://pith.science/api/pith-number/435ZDOSXG4UVUAGYKL7YGEDH6Y/graph.json","fetch_events":"https://pith.science/api/pith-number/435ZDOSXG4UVUAGYKL7YGEDH6Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y/action/storage_attestation","attest_author":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y/action/author_attestation","sign_citation":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y/action/citation_signature","submit_replication":"https://pith.science/pith/435ZDOSXG4UVUAGYKL7YGEDH6Y/action/replication_record"}},"created_at":"2026-05-18T00:26:36.337216+00:00","updated_at":"2026-05-18T00:26:36.337216+00:00"}