{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:H4K2MPU6XXXM2QAAR6FYIERQE3","short_pith_number":"pith:H4K2MPU6","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"},"canonical_sha256":"3f15a63e9ebdeecd40008f8b84123026da948486259ea2a63bfabf00e7a47b70","source":{"kind":"arxiv","id":"1906.10563","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10563","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10563v1","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10563","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"H4K2MPU6XXXM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"H4K2MPU6XXXM2QAA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"H4K2MPU6","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:H4K2MPU6XXXM2QAAR6FYIERQE3","target":"record","payload":{"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"},"canonical_sha256":"3f15a63e9ebdeecd40008f8b84123026da948486259ea2a63bfabf00e7a47b70","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"},"source_kind":"arxiv","source_id":"1906.10563","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FwlPjhYLH3hDXlo8/47prTjk1FMx1l6qebCo4Uky44G3/HQ8JEoUbGMXD4yj+wf64zQUp43/h5RYGpg0EdNqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:58:36.175015Z"},"content_sha256":"978dc029b0be7923e7045dd3c0d1559511a9e0fb7f6dd959b129a158c6e2e484","schema_version":"1.0","event_id":"sha256:978dc029b0be7923e7045dd3c0d1559511a9e0fb7f6dd959b129a158c6e2e484"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:H4K2MPU6XXXM2QAAR6FYIERQE3","target":"graph","payload":{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10563","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bf4E+C4EnDBUN5dElt2ZGF2C6UQ8qv/ctVN/DazkOyWspC1KsjuAajbi3iZcbf3Wz5xzpp5REBZojxWnyMU8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:58:36.175751Z"},"content_sha256":"a7e0afd46dbefb50bbba0b349611ee2a2bec78999aaf3a08a5267c8f68e65405","schema_version":"1.0","event_id":"sha256:a7e0afd46dbefb50bbba0b349611ee2a2bec78999aaf3a08a5267c8f68e65405"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4K2MPU6XXXM2QAAR6FYIERQE3/bundle.json","state_url":"https://pith.science/pith/H4K2MPU6XXXM2QAAR6FYIERQE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4K2MPU6XXXM2QAAR6FYIERQE3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T02:58:36Z","links":{"resolver":"https://pith.science/pith/H4K2MPU6XXXM2QAAR6FYIERQE3","bundle":"https://pith.science/pith/H4K2MPU6XXXM2QAAR6FYIERQE3/bundle.json","state":"https://pith.science/pith/H4K2MPU6XXXM2QAAR6FYIERQE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4K2MPU6XXXM2QAAR6FYIERQE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:H4K2MPU6XXXM2QAAR6FYIERQE3","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":"193582e4809e192058241b1586f7d2c3b28ce1b2e8408c05c7d8088ff42c6483","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-06-25T14:30:28Z","title_canon_sha256":"d7261ad92dab1e36026b97757bf6cdd9b220bf39fea0166f0fea4eb984bb0f88"},"schema_version":"1.0","source":{"id":"1906.10563","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10563","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10563v1","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10563","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"H4K2MPU6XXXM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"H4K2MPU6XXXM2QAA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"H4K2MPU6","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:a7e0afd46dbefb50bbba0b349611ee2a2bec78999aaf3a08a5267c8f68e65405","target":"graph","created_at":"2026-05-17T23:42:15Z","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":"Let $S$ be a rank-one symmetric space of non-compact type and let $X$ be a $\\text{CAT}(-1)$ space. 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","authors_text":"Alessio Savini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-06-25T14:30:28Z","title":"Asymptotically Moebius maps and rigidity for the hyperbolic plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10563","kind":"arxiv","version":1},"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":"sha256:978dc029b0be7923e7045dd3c0d1559511a9e0fb7f6dd959b129a158c6e2e484","target":"record","created_at":"2026-05-17T23:42:15Z","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":"193582e4809e192058241b1586f7d2c3b28ce1b2e8408c05c7d8088ff42c6483","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-06-25T14:30:28Z","title_canon_sha256":"d7261ad92dab1e36026b97757bf6cdd9b220bf39fea0166f0fea4eb984bb0f88"},"schema_version":"1.0","source":{"id":"1906.10563","kind":"arxiv","version":1}},"canonical_sha256":"3f15a63e9ebdeecd40008f8b84123026da948486259ea2a63bfabf00e7a47b70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f15a63e9ebdeecd40008f8b84123026da948486259ea2a63bfabf00e7a47b70","first_computed_at":"2026-05-17T23:42:15.961045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:15.961045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KaaIv+Nzd7s4etpywaB3E5JNfRqpf+yOGcHMAZ42LhapZvcU+E97AOj8u9/w2M8W/3ZflLy+mawgOu+Qk6BGBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:15.961775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10563","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:978dc029b0be7923e7045dd3c0d1559511a9e0fb7f6dd959b129a158c6e2e484","sha256:a7e0afd46dbefb50bbba0b349611ee2a2bec78999aaf3a08a5267c8f68e65405"],"state_sha256":"524cf5abfad2f8345ae8012dc367b417aa35e25aa12b83341f44c558944c1135"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEeRXPdrWX3EyLHjYaq8o635cEW1Bi1+vrUNfXoetfy+4O3lRBsbQMk4Hn+MxUV7+gmZzXzq8Gg18Ldo9apLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:58:36.179987Z","bundle_sha256":"0a35effc8d7825967972df4de812cfdb77b7c79b5af9454a996c96a1ef335ade"}}