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However, a similar result does not hold in the tree T. Let W be a reduced and cyclically reduced word in $\\pi_1(M) = <x,y>$. We construct several examples of triangles in T formed by distinct axes in T stabilized by conjugates of W such that an edge in those triangles is longer th"},"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":"1806.04018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-08T17:43:36Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3ef65dbd0583f4cbd6278734da39f68208b0ccb0eedb9c564e6272566edca117","abstract_canon_sha256":"a98939d71e8a2db634dc76a9839fdef06f8cddfce6f0c4675d6bce9211f97793"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:23.301143Z","signature_b64":"21itHHWeFPDRz7x2t3tr8iNN0CbQArO1obZZza8RocO+6IbKdiRjyCQMcnuhKVEqDdo+NXWN4hlH6sUeNw3VDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75fcf75f2b51afbf17e9b54e7c16ce8d0c97922cb97e4a6e207bfad6510b385e","last_reissued_at":"2026-05-18T00:01:23.300781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:23.300781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjugate Words and Intersections of Geodesics in $H^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Rita Gitik","submitted_at":"2018-06-08T17:43:36Z","abstract_excerpt":"We investigate intersections of geodesic lines in $H^2$ and in an associated tree T, proving the following result. 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We construct several examples of triangles in T formed by distinct axes in T stabilized by conjugates of W such that an edge in those triangles is longer th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04018","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":"1806.04018","created_at":"2026-05-18T00:01:23.300837+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.04018v1","created_at":"2026-05-18T00:01:23.300837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04018","created_at":"2026-05-18T00:01:23.300837+00:00"},{"alias_kind":"pith_short_12","alias_value":"OX6POXZLKGX3","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OX6POXZLKGX36F7J","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OX6POXZL","created_at":"2026-05-18T12:32:43.782077+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/OX6POXZLKGX36F7JWVHHYFWORU","json":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU.json","graph_json":"https://pith.science/api/pith-number/OX6POXZLKGX36F7JWVHHYFWORU/graph.json","events_json":"https://pith.science/api/pith-number/OX6POXZLKGX36F7JWVHHYFWORU/events.json","paper":"https://pith.science/paper/OX6POXZL"},"agent_actions":{"view_html":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU","download_json":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU.json","view_paper":"https://pith.science/paper/OX6POXZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.04018&json=true","fetch_graph":"https://pith.science/api/pith-number/OX6POXZLKGX36F7JWVHHYFWORU/graph.json","fetch_events":"https://pith.science/api/pith-number/OX6POXZLKGX36F7JWVHHYFWORU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU/action/storage_attestation","attest_author":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU/action/author_attestation","sign_citation":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU/action/citation_signature","submit_replication":"https://pith.science/pith/OX6POXZLKGX36F7JWVHHYFWORU/action/replication_record"}},"created_at":"2026-05-18T00:01:23.300837+00:00","updated_at":"2026-05-18T00:01:23.300837+00:00"}