{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:W2U4NGU26QDPGCHWOTNV7SMGGE","short_pith_number":"pith:W2U4NGU2","schema_version":"1.0","canonical_sha256":"b6a9c69a9af406f308f674db5fc986312868acab78085a54146c5d66072ab875","source":{"kind":"arxiv","id":"0910.4569","version":3},"attestation_state":"computed","paper":{"title":"Assouad-Nagata dimension of connected Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.GR","authors_text":"I. Peng, J. Higes","submitted_at":"2009-10-23T19:18:28Z","abstract_excerpt":"We prove that the asymptotic Assouad-Nagata dimension of a connected Lie group $G$ equipped with a left-invariant Riemannian metric coincides with its topological dimension of $G/C$ where $C$ is a maximal compact subgroup. To prove it we will compute the Assouad-Nagata dimension of connected solvable Lie groups and semisimple Lie groups. As a consequence we show that the asymptotic Assouad-Nagata dimension of a polycyclic group equipped with a word metric is equal to its Hirsch length and that some wreath-type finitely generated groups can not be quasi-isometric to any cocompact lattice on a c"},"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":"0910.4569","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-23T19:18:28Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"c1b556068c87f51b7c6d7d01d6cff82218b50026f948ea934efaf18ecdc492bc","abstract_canon_sha256":"7ecebc74b85f55294f01403ea71b2c537f3963050584d23c6ea68e85426131fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:20.531440Z","signature_b64":"X6BxhUI8+DS/b1eBR3I1ePTxaoNQUd/mYWf/6Ai2HxD3UJn8GKscXBpUO3ZCCYZO551QzzH18W9frTVBChOzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6a9c69a9af406f308f674db5fc986312868acab78085a54146c5d66072ab875","last_reissued_at":"2026-05-18T04:40:20.530797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:20.530797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Assouad-Nagata dimension of connected Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.GR","authors_text":"I. Peng, J. Higes","submitted_at":"2009-10-23T19:18:28Z","abstract_excerpt":"We prove that the asymptotic Assouad-Nagata dimension of a connected Lie group $G$ equipped with a left-invariant Riemannian metric coincides with its topological dimension of $G/C$ where $C$ is a maximal compact subgroup. To prove it we will compute the Assouad-Nagata dimension of connected solvable Lie groups and semisimple Lie groups. As a consequence we show that the asymptotic Assouad-Nagata dimension of a polycyclic group equipped with a word metric is equal to its Hirsch length and that some wreath-type finitely generated groups can not be quasi-isometric to any cocompact lattice on a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4569","kind":"arxiv","version":3},"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":"0910.4569","created_at":"2026-05-18T04:40:20.530887+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.4569v3","created_at":"2026-05-18T04:40:20.530887+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4569","created_at":"2026-05-18T04:40:20.530887+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2U4NGU26QDP","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2U4NGU26QDPGCHW","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2U4NGU2","created_at":"2026-05-18T12:26:02.257875+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/W2U4NGU26QDPGCHWOTNV7SMGGE","json":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE.json","graph_json":"https://pith.science/api/pith-number/W2U4NGU26QDPGCHWOTNV7SMGGE/graph.json","events_json":"https://pith.science/api/pith-number/W2U4NGU26QDPGCHWOTNV7SMGGE/events.json","paper":"https://pith.science/paper/W2U4NGU2"},"agent_actions":{"view_html":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE","download_json":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE.json","view_paper":"https://pith.science/paper/W2U4NGU2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.4569&json=true","fetch_graph":"https://pith.science/api/pith-number/W2U4NGU26QDPGCHWOTNV7SMGGE/graph.json","fetch_events":"https://pith.science/api/pith-number/W2U4NGU26QDPGCHWOTNV7SMGGE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE/action/storage_attestation","attest_author":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE/action/author_attestation","sign_citation":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE/action/citation_signature","submit_replication":"https://pith.science/pith/W2U4NGU26QDPGCHWOTNV7SMGGE/action/replication_record"}},"created_at":"2026-05-18T04:40:20.530887+00:00","updated_at":"2026-05-18T04:40:20.530887+00:00"}