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We classify ${\\rm SU}(n,1)$ conjugation orbits of pairs of loxodromic elements in ${\\rm SU}(n,1)$."},"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":"1705.10469","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-30T06:29:24Z","cross_cats_sorted":[],"title_canon_sha256":"1b3b573d0a5fddcff4cc8e02744d2a8bab7f2165dae35c515832cd8f2086e02f","abstract_canon_sha256":"f87e61dea17e03d772474d7a09da79c5333245d03d079350e42f6e7f4857fb61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:22.017173Z","signature_b64":"njNKI5aMpVhNbLT1f6bDt6VQNrr2BkQ9ARTbQOCjKY1pPoyCcGKg1D3x9Ia/r9qEQndTVBYTBThuAJciUWTSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6279a6a963b7dd42efd234ca1320f86ca0c835e6f4eb09e7d3b2e0b6b27cd3bf","last_reissued_at":"2026-05-18T00:13:22.016439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:22.016439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjugation Orbits of Loxodromic Pairs in SU(n,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Krishnendu Gongopadhyay, Shiv Parsad","submitted_at":"2017-05-30T06:29:24Z","abstract_excerpt":"Let ${\\bf H}_{\\mathbb C}^n$ be the $n$-dimensional complex hyperbolic space and ${\\rm SU}(n,1)$ be the (holomorphic) isometry group. An element $g$ in ${\\rm SU}(n,1)$ is called loxodromic or hyperbolic if it has exactly two fixed points on the boundary $\\partial {\\bf H}_{\\mathbb C}^n$. We classify ${\\rm SU}(n,1)$ conjugation orbits of pairs of loxodromic elements in ${\\rm SU}(n,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10469","kind":"arxiv","version":4},"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":"1705.10469","created_at":"2026-05-18T00:13:22.016559+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.10469v4","created_at":"2026-05-18T00:13:22.016559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10469","created_at":"2026-05-18T00:13:22.016559+00:00"},{"alias_kind":"pith_short_12","alias_value":"MJ42NKLDW7OU","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MJ42NKLDW7OUF36S","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MJ42NKLD","created_at":"2026-05-18T12:31:31.346846+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/MJ42NKLDW7OUF36SGTFBGIHYNS","json":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS.json","graph_json":"https://pith.science/api/pith-number/MJ42NKLDW7OUF36SGTFBGIHYNS/graph.json","events_json":"https://pith.science/api/pith-number/MJ42NKLDW7OUF36SGTFBGIHYNS/events.json","paper":"https://pith.science/paper/MJ42NKLD"},"agent_actions":{"view_html":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS","download_json":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS.json","view_paper":"https://pith.science/paper/MJ42NKLD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.10469&json=true","fetch_graph":"https://pith.science/api/pith-number/MJ42NKLDW7OUF36SGTFBGIHYNS/graph.json","fetch_events":"https://pith.science/api/pith-number/MJ42NKLDW7OUF36SGTFBGIHYNS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS/action/storage_attestation","attest_author":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS/action/author_attestation","sign_citation":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS/action/citation_signature","submit_replication":"https://pith.science/pith/MJ42NKLDW7OUF36SGTFBGIHYNS/action/replication_record"}},"created_at":"2026-05-18T00:13:22.016559+00:00","updated_at":"2026-05-18T00:13:22.016559+00:00"}