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A well-known result by Bourdon states that if a topological embedding $\\varphi: \\partial_\\infty S \\rightarrow \\partial_\\infty X$ respects cross ratios, that means $\\text{cr}_S( \\xi_0,\\eta_0,\\xi_1,\\eta_1)=\\text{cr}_X( \\varphi(\\xi_0),\\varphi(\\eta_0),\\varphi(\\xi_1),\\varphi(\\eta_1))$ for every $\\xi_0,\\eta_0,\\xi_1,\\eta_1 \\in \\partial_\\infty S$, then $\\varphi$ is induced by an isometric embedding of $S$ into $X$.\n  We generalize this result when $S=\\mathbb{H}^2$ is the real hyperbolic plane as it follo"},"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":"1906.10563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-06-25T14:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"d7261ad92dab1e36026b97757bf6cdd9b220bf39fea0166f0fea4eb984bb0f88","abstract_canon_sha256":"193582e4809e192058241b1586f7d2c3b28ce1b2e8408c05c7d8088ff42c6483"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:15.961775Z","signature_b64":"KaaIv+Nzd7s4etpywaB3E5JNfRqpf+yOGcHMAZ42LhapZvcU+E97AOj8u9/w2M8W/3ZflLy+mawgOu+Qk6BGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f15a63e9ebdeecd40008f8b84123026da948486259ea2a63bfabf00e7a47b70","last_reissued_at":"2026-05-17T23:42:15.961045Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:15.961045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotically Moebius maps and rigidity for the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alessio Savini","submitted_at":"2019-06-25T14:30:28Z","abstract_excerpt":"Let $S$ be a rank-one symmetric space of non-compact type and let $X$ be a $\\text{CAT}(-1)$ space. 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