{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S6OC24NF63W7HWQ3YHGD2WZPVF","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":"81ad4517d8c09b224df0130d38bc5aef1f37c6ccc82f5e3d6bcbe88fbfe2a0ec","cross_cats_sorted":["math.DS","math.GR","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-10T17:43:15Z","title_canon_sha256":"70443edcc7b2c99024546adecf6526c78b008ad01f924d540c3ab0adee56ea32"},"schema_version":"1.0","source":{"id":"1707.02960","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02960","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02960v2","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02960","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"S6OC24NF63W7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S6OC24NF63W7HWQ3","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S6OC24NF","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:a2ec8795d7284953d5892dbe4588ab48a84202c4cbb354ecf87d0e963a01e8f2","target":"graph","created_at":"2026-05-17T23:48:57Z","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 prove that if a quasi-isometry of warped cones is induced by a map between the base spaces of the cones, the actions must be conjugate by this map. The converse is false in general, conjugacy of actions is not sufficient for quasi-isometry of the respective warped cones. For a general quasi-isometry of warped cones, using the asymptotically faithful covering constructed in a previous work with Jianchao Wu, we deduce that the two groups are quasi-isometric after taking Cartesian products with suitable powers of the integers.\n  Secondly, we characterise geometric properties of a group (coarse","authors_text":"Damian Sawicki","cross_cats":["math.DS","math.GR","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-10T17:43:15Z","title":"Warped cones, (non-)rigidity, and piecewise properties, with a joint appendix with Dawid Kielak"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02960","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":"sha256:3c762e1df9b284edcd0feee2223367e1d772e9a84b21bc6008e4b2011ca61c46","target":"record","created_at":"2026-05-17T23:48:57Z","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":"81ad4517d8c09b224df0130d38bc5aef1f37c6ccc82f5e3d6bcbe88fbfe2a0ec","cross_cats_sorted":["math.DS","math.GR","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-10T17:43:15Z","title_canon_sha256":"70443edcc7b2c99024546adecf6526c78b008ad01f924d540c3ab0adee56ea32"},"schema_version":"1.0","source":{"id":"1707.02960","kind":"arxiv","version":2}},"canonical_sha256":"979c2d71a5f6edf3da1bc1cc3d5b2fa97dfcd8d79af2de79e20df06ae70466d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979c2d71a5f6edf3da1bc1cc3d5b2fa97dfcd8d79af2de79e20df06ae70466d3","first_computed_at":"2026-05-17T23:48:57.475181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:57.475181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yGOoMmCf/9W6VJck/WUYYP8rzLP5/KECNIdEQT1vGB8/9bAfi3X70sjZmSK6PjWhWhSFhuPVnUBerIcAbLPLDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:57.475667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02960","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c762e1df9b284edcd0feee2223367e1d772e9a84b21bc6008e4b2011ca61c46","sha256:a2ec8795d7284953d5892dbe4588ab48a84202c4cbb354ecf87d0e963a01e8f2"],"state_sha256":"7cacba0e686774ea32b24d17f1dd782eba825ae7cda38ff9f3ee42cb70b4253a"}