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For any $0<\\theta <1$, denote by $X_\\theta = [X_0, X_1]_\\theta$ and $Y_\\theta = [Y_0, Y_1]_\\theta$ the complex interpolation spaces and by $B(r, X_\\theta)$, $0 \\le \\theta \\le 1,$ the open ball of radius $r>0$ in $X_\\theta$, centered at zero. Then for any analytic map $\\Phi: B(r, X_0) \\to Y_0+ Y_1$ such that $\\Phi: B(r, X_0)\\to Y_0$ and $\\Phi: B(c^{-1}r, X_1)\\to Y_1$ are continuous and bounded by constants $M_0$ and $M_1$, respecti"},"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":"1405.4253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-16T17:47:20Z","cross_cats_sorted":[],"title_canon_sha256":"84869231c187c6c0178e10f70b2abf931551a2e9ad32f209636f183f4d46d0b2","abstract_canon_sha256":"d4ae2601b581659228361692391908ece8a69532d029f48f689d3c9dc5f4172c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.822595Z","signature_b64":"x8T4yHlqhZ8ga9EOnUy0RiANGsA79iVZQijG9Um6QlRRbtW94jkV8Xr1ev/LRTA7YWBKqFliW9/KmXBtD1GOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b014f3ecaa751d59e2f41703343728febd83f04b74a582752f48943b164a092","last_reissued_at":"2026-05-18T02:51:42.822089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.822089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpolation of nonlinear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Savchuk, A. Shkalikov, P. Topalov, T. Kappeler","submitted_at":"2014-05-16T17:47:20Z","abstract_excerpt":"Let $(X_0, X_1)$ and $(Y_0, Y_1)$ be complex Banach couples and assume that $X_1\\subseteq X_0$ with norms satisfying $\\|x\\|_{X_0} \\le c\\|x\\|_{X_1}$ for some $c > 0$. For any $0<\\theta <1$, denote by $X_\\theta = [X_0, X_1]_\\theta$ and $Y_\\theta = [Y_0, Y_1]_\\theta$ the complex interpolation spaces and by $B(r, X_\\theta)$, $0 \\le \\theta \\le 1,$ the open ball of radius $r>0$ in $X_\\theta$, centered at zero. Then for any analytic map $\\Phi: B(r, X_0) \\to Y_0+ Y_1$ such that $\\Phi: B(r, X_0)\\to Y_0$ and $\\Phi: B(c^{-1}r, X_1)\\to Y_1$ are continuous and bounded by constants $M_0$ and $M_1$, respecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4253","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":"1405.4253","created_at":"2026-05-18T02:51:42.822167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.4253v1","created_at":"2026-05-18T02:51:42.822167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4253","created_at":"2026-05-18T02:51:42.822167+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMAU6PWKU5I5","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMAU6PWKU5I5LHRP","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMAU6PWK","created_at":"2026-05-18T12:28:33.132498+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/JMAU6PWKU5I5LHRPIFYDGQ3SR7","json":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7.json","graph_json":"https://pith.science/api/pith-number/JMAU6PWKU5I5LHRPIFYDGQ3SR7/graph.json","events_json":"https://pith.science/api/pith-number/JMAU6PWKU5I5LHRPIFYDGQ3SR7/events.json","paper":"https://pith.science/paper/JMAU6PWK"},"agent_actions":{"view_html":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7","download_json":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7.json","view_paper":"https://pith.science/paper/JMAU6PWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.4253&json=true","fetch_graph":"https://pith.science/api/pith-number/JMAU6PWKU5I5LHRPIFYDGQ3SR7/graph.json","fetch_events":"https://pith.science/api/pith-number/JMAU6PWKU5I5LHRPIFYDGQ3SR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7/action/storage_attestation","attest_author":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7/action/author_attestation","sign_citation":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7/action/citation_signature","submit_replication":"https://pith.science/pith/JMAU6PWKU5I5LHRPIFYDGQ3SR7/action/replication_record"}},"created_at":"2026-05-18T02:51:42.822167+00:00","updated_at":"2026-05-18T02:51:42.822167+00:00"}