{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:PCZDXV5QE3MUJGOB2IN5MQWRAO","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":"55a57452ee7587e0a25a9376d824f82297ec17194583abad1a2a2183a82c7c02","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2004-11-02T01:58:05Z","title_canon_sha256":"b37196f395cc53b242ac6171f1af1ca888c5640d6ff2fd596c1dea251afc9b51"},"schema_version":"1.0","source":{"id":"math/0411039","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411039","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411039v3","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411039","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"PCZDXV5QE3MU","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"PCZDXV5QE3MUJGOB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"PCZDXV5Q","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:0f636614816c9fbfa2c74eb5a48c09afe8608fd52d59165ba5e55e2240372a6f","target":"graph","created_at":"2026-05-18T04:18:33Z","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 generalize the small cancellation theory over hyperbolic groups developed by Olshanskii to the case of relatively hyperbolic groups. This allows us to construct infinite finitely generated groups with exactly $n$ conjugacy classes for every $n\\ge 2$. In particular, we give the affirmative answer to the well--known question of the existence of a finitely generated group $G$ other than $\\mathbb Z/2\\mathbb Z$ such that all nontrivial elements of $G$ are conjugate.","authors_text":"D.V. Osin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2004-11-02T01:58:05Z","title":"Small cancellations over relatively hyperbolic groups and embedding theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411039","kind":"arxiv","version":3},"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":"sha256:8f0aac9b851cb23bed1ade9490d9d2d775451e10343cf04399c46124ddc2e9fb","target":"record","created_at":"2026-05-18T04:18:33Z","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":"55a57452ee7587e0a25a9376d824f82297ec17194583abad1a2a2183a82c7c02","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2004-11-02T01:58:05Z","title_canon_sha256":"b37196f395cc53b242ac6171f1af1ca888c5640d6ff2fd596c1dea251afc9b51"},"schema_version":"1.0","source":{"id":"math/0411039","kind":"arxiv","version":3}},"canonical_sha256":"78b23bd7b026d94499c1d21bd642d10383072ebbafa80b1e92e443de5f889c1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78b23bd7b026d94499c1d21bd642d10383072ebbafa80b1e92e443de5f889c1f","first_computed_at":"2026-05-18T04:18:33.433679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:33.433679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XyTWpO3rhXAueICS3EsjPe8fNhInMQNp0mo7/739kRm4LYDbogyKzIuxkCIAov3beL1JUUdAHtAcHPCC7N2mDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:33.434393Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0411039","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f0aac9b851cb23bed1ade9490d9d2d775451e10343cf04399c46124ddc2e9fb","sha256:0f636614816c9fbfa2c74eb5a48c09afe8608fd52d59165ba5e55e2240372a6f"],"state_sha256":"084cfb27b5fdf443bc48c23f65156b94c28feacc4b65af87d65fdfabdfbc0ff8"}