{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:TQEJFHNUHDAC7VKTDYFUTHF727","short_pith_number":"pith:TQEJFHNU","schema_version":"1.0","canonical_sha256":"9c08929db438c02fd5531e0b499cbfd7fda95ed8f1a835384b529f659ddfb2a8","source":{"kind":"arxiv","id":"math/0201312","version":1},"attestation_state":"computed","paper":{"title":"Group splittings and asymptotic topology","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Panos Papasoglu","submitted_at":"2002-01-31T12:05:50Z","abstract_excerpt":"It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splittings are preserved under quasi-isometries when the vertex groups are fundamental groups of aspherical manifolds (or more generally `coarse PD(n)-groups') and the edge groups are `smaller' than the vertex 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":"math/0201312","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2002-01-31T12:05:50Z","cross_cats_sorted":[],"title_canon_sha256":"f57808da8fdf203b464dc62c9104435cb4f44f0de4383e1cb0a16507eef207dd","abstract_canon_sha256":"cc9b886d95f31457a60710018cc34c1f395ddc2252c9921601fd3ba5673da44c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.795874Z","signature_b64":"knNneGDURFBEB6Yu5jnNYfZFcag8k3xL+G2OpBZXaHKRFRYV9ljbLesFOyQiBjjbeVCHm/RF24KT4as4+SnwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c08929db438c02fd5531e0b499cbfd7fda95ed8f1a835384b529f659ddfb2a8","last_reissued_at":"2026-05-18T01:05:29.795340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.795340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Group splittings and asymptotic topology","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Panos Papasoglu","submitted_at":"2002-01-31T12:05:50Z","abstract_excerpt":"It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splittings are preserved under quasi-isometries when the vertex groups are fundamental groups of aspherical manifolds (or more generally `coarse PD(n)-groups') and the edge groups are `smaller' than the vertex groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201312","kind":"arxiv","version":1},"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":"math/0201312","created_at":"2026-05-18T01:05:29.795422+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0201312v1","created_at":"2026-05-18T01:05:29.795422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201312","created_at":"2026-05-18T01:05:29.795422+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQEJFHNUHDAC","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQEJFHNUHDAC7VKT","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQEJFHNU","created_at":"2026-05-18T12:25:51.375804+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/TQEJFHNUHDAC7VKTDYFUTHF727","json":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727.json","graph_json":"https://pith.science/api/pith-number/TQEJFHNUHDAC7VKTDYFUTHF727/graph.json","events_json":"https://pith.science/api/pith-number/TQEJFHNUHDAC7VKTDYFUTHF727/events.json","paper":"https://pith.science/paper/TQEJFHNU"},"agent_actions":{"view_html":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727","download_json":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727.json","view_paper":"https://pith.science/paper/TQEJFHNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0201312&json=true","fetch_graph":"https://pith.science/api/pith-number/TQEJFHNUHDAC7VKTDYFUTHF727/graph.json","fetch_events":"https://pith.science/api/pith-number/TQEJFHNUHDAC7VKTDYFUTHF727/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727/action/storage_attestation","attest_author":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727/action/author_attestation","sign_citation":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727/action/citation_signature","submit_replication":"https://pith.science/pith/TQEJFHNUHDAC7VKTDYFUTHF727/action/replication_record"}},"created_at":"2026-05-18T01:05:29.795422+00:00","updated_at":"2026-05-18T01:05:29.795422+00:00"}