{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:LSOGHRL5DJE2IIECDZB2LVTUMP","short_pith_number":"pith:LSOGHRL5","schema_version":"1.0","canonical_sha256":"5c9c63c57d1a49a420821e43a5d67463ff0b6b7fdf30590124571dae2b408aaa","source":{"kind":"arxiv","id":"0709.2113","version":2},"attestation_state":"computed","paper":{"title":"Combination of quasiconvex subgroups of relatively hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Eduardo Martinez-Pedroza","submitted_at":"2007-09-13T17:01:21Z","abstract_excerpt":"For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups $Q$ and $R$ is quasiconvex and isomorphic to $Q \\ast_{Q\\cap R} R$. Our results generalized known combination theorems for quasiconvex subgroups of word-hyperbolic groups. Some applications are presented."},"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":"0709.2113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-09-13T17:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"89f291c2d2b4ddad22ae054ba2adea4f0b78205c67fb84d816d6fd5f1695c785","abstract_canon_sha256":"820a3673114225286a9a861a28cd27876db938363da81b191e465dadec4f335c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:49.123714Z","signature_b64":"GVohs4RnMYLMcRGvjBrlAWeN4KS+YQmOXlIaIiG2ILmwp7g476JSsLhI6mrlQE15PGZ+ugNtni/vz7guuBTeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c9c63c57d1a49a420821e43a5d67463ff0b6b7fdf30590124571dae2b408aaa","last_reissued_at":"2026-05-18T01:20:49.123313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:49.123313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combination of quasiconvex subgroups of relatively hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Eduardo Martinez-Pedroza","submitted_at":"2007-09-13T17:01:21Z","abstract_excerpt":"For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups $Q$ and $R$ is quasiconvex and isomorphic to $Q \\ast_{Q\\cap R} R$. Our results generalized known combination theorems for quasiconvex subgroups of word-hyperbolic groups. Some applications are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2113","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":"0709.2113","created_at":"2026-05-18T01:20:49.123389+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.2113v2","created_at":"2026-05-18T01:20:49.123389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2113","created_at":"2026-05-18T01:20:49.123389+00:00"},{"alias_kind":"pith_short_12","alias_value":"LSOGHRL5DJE2","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"LSOGHRL5DJE2IIEC","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"LSOGHRL5","created_at":"2026-05-18T12:25:55.427421+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/LSOGHRL5DJE2IIECDZB2LVTUMP","json":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP.json","graph_json":"https://pith.science/api/pith-number/LSOGHRL5DJE2IIECDZB2LVTUMP/graph.json","events_json":"https://pith.science/api/pith-number/LSOGHRL5DJE2IIECDZB2LVTUMP/events.json","paper":"https://pith.science/paper/LSOGHRL5"},"agent_actions":{"view_html":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP","download_json":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP.json","view_paper":"https://pith.science/paper/LSOGHRL5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.2113&json=true","fetch_graph":"https://pith.science/api/pith-number/LSOGHRL5DJE2IIECDZB2LVTUMP/graph.json","fetch_events":"https://pith.science/api/pith-number/LSOGHRL5DJE2IIECDZB2LVTUMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP/action/storage_attestation","attest_author":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP/action/author_attestation","sign_citation":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP/action/citation_signature","submit_replication":"https://pith.science/pith/LSOGHRL5DJE2IIECDZB2LVTUMP/action/replication_record"}},"created_at":"2026-05-18T01:20:49.123389+00:00","updated_at":"2026-05-18T01:20:49.123389+00:00"}