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If $\\phi: (\\Omega_1, d^K_{\\Omega_1}) \\rightarrow (\\Omega_2, d^K_{\\Omega_2})$ is an isometry, i.e. $ d^K_\\Omega_{n_2}(f(\\zeta),f(\\eta)) = d^K_{n_1} (\\zeta,\\eta)$ for all $\\zeta,\\eta \\in \\Omega_1,$ then $\\phi$ is either holomorphic or anti-holomorphic."},"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":"1201.4944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-01-24T10:42:38Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"21f21c87e1c5a73a7985b8a9bf16da3ecd2ec80224698c14f1ec5cb46d35013a","abstract_canon_sha256":"2445ef9d743f2647ca2cd37758e204f80c7c2056b6554bbd33d16dda4a816a38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:56.613592Z","signature_b64":"a7TaJpJmsT8gV7bzPj3BD7J2gA8iJcYAoBuTmQYM34vPjIueqEj6acbdobJdi4nph7OvVTJbzrdU9+bd5H+3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f11d583ba9abd79face2865a2da105c3576cc28f172cd1671caf05c9dd7029f9","last_reissued_at":"2026-05-18T04:03:56.613065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:56.613065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Totally geodesic discs in strongly convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Harish Seshadri, Herve Gaussier","submitted_at":"2012-01-24T10:42:38Z","abstract_excerpt":"We prove that Kobayashi isometries between strongly convex domains are holomorphic or anti-holomorphic.\n  More precisely, let $n_1, n_2$ be positive integers and let $\\Omega_i \\subset \\C^{n_i}, \\ i=1,2$, be bounded $C^3$ strongly convex domains. If $\\phi: (\\Omega_1, d^K_{\\Omega_1}) \\rightarrow (\\Omega_2, d^K_{\\Omega_2})$ is an isometry, i.e. $ d^K_\\Omega_{n_2}(f(\\zeta),f(\\eta)) = d^K_{n_1} (\\zeta,\\eta)$ for all $\\zeta,\\eta \\in \\Omega_1,$ then $\\phi$ is either holomorphic or anti-holomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4944","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":"1201.4944","created_at":"2026-05-18T04:03:56.613147+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.4944v1","created_at":"2026-05-18T04:03:56.613147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4944","created_at":"2026-05-18T04:03:56.613147+00:00"},{"alias_kind":"pith_short_12","alias_value":"6EOVQO5JVPLZ","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6EOVQO5JVPLZ7LHC","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6EOVQO5J","created_at":"2026-05-18T12:26:56.085431+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/6EOVQO5JVPLZ7LHCQZNC3IIFYN","json":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN.json","graph_json":"https://pith.science/api/pith-number/6EOVQO5JVPLZ7LHCQZNC3IIFYN/graph.json","events_json":"https://pith.science/api/pith-number/6EOVQO5JVPLZ7LHCQZNC3IIFYN/events.json","paper":"https://pith.science/paper/6EOVQO5J"},"agent_actions":{"view_html":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN","download_json":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN.json","view_paper":"https://pith.science/paper/6EOVQO5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.4944&json=true","fetch_graph":"https://pith.science/api/pith-number/6EOVQO5JVPLZ7LHCQZNC3IIFYN/graph.json","fetch_events":"https://pith.science/api/pith-number/6EOVQO5JVPLZ7LHCQZNC3IIFYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN/action/storage_attestation","attest_author":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN/action/author_attestation","sign_citation":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN/action/citation_signature","submit_replication":"https://pith.science/pith/6EOVQO5JVPLZ7LHCQZNC3IIFYN/action/replication_record"}},"created_at":"2026-05-18T04:03:56.613147+00:00","updated_at":"2026-05-18T04:03:56.613147+00:00"}