{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V2ZLH2QYEO4HNOTUIO4NCK6DK7","short_pith_number":"pith:V2ZLH2QY","schema_version":"1.0","canonical_sha256":"aeb2b3ea1823b876ba7443b8d12bc357e935ad11c2bc7e0bd186d6a267011e57","source":{"kind":"arxiv","id":"1802.09137","version":2},"attestation_state":"computed","paper":{"title":"Conformality of quasiconformal mappings at a point, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mitsuhiro Shishikura","submitted_at":"2018-02-26T02:45:17Z","abstract_excerpt":"We present a new and simple proof of Teichm\\\"uller-Wittich-Belinskii's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point. Known proofs gave separate estimates for the radial and angular variations, but our proof unifies them using Gr\\\"otzsch-type inequality for the variation of cross-ratio of four points on the Riemann sphere. We also give a sufficient condition for $C^{1+\\alpha}$-conformality"},"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":"1802.09137","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-26T02:45:17Z","cross_cats_sorted":[],"title_canon_sha256":"ffd548fffdf32c85694ecdfc2ace48c3f1d520959f32a57c5df0ee592ffa3154","abstract_canon_sha256":"cf674412cef35658b7bf173a67540612c81b9d519d4214b74f2531e8e300953d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:18.555965Z","signature_b64":"nYX4WxE2ec65hBp5tP/qDkn2qGQUCZL39xApe+3O1bBF9pmFw/ixvufZaqWalpccn+uHpw1D1KQFENz33XUKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeb2b3ea1823b876ba7443b8d12bc357e935ad11c2bc7e0bd186d6a267011e57","last_reissued_at":"2026-05-18T00:17:18.555504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:18.555504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformality of quasiconformal mappings at a point, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mitsuhiro Shishikura","submitted_at":"2018-02-26T02:45:17Z","abstract_excerpt":"We present a new and simple proof of Teichm\\\"uller-Wittich-Belinskii's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point. Known proofs gave separate estimates for the radial and angular variations, but our proof unifies them using Gr\\\"otzsch-type inequality for the variation of cross-ratio of four points on the Riemann sphere. We also give a sufficient condition for $C^{1+\\alpha}$-conformality"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09137","kind":"arxiv","version":2},"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":"1802.09137","created_at":"2026-05-18T00:17:18.555562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.09137v2","created_at":"2026-05-18T00:17:18.555562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09137","created_at":"2026-05-18T00:17:18.555562+00:00"},{"alias_kind":"pith_short_12","alias_value":"V2ZLH2QYEO4H","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"V2ZLH2QYEO4HNOTU","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"V2ZLH2QY","created_at":"2026-05-18T12:32:56.356000+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/V2ZLH2QYEO4HNOTUIO4NCK6DK7","json":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7.json","graph_json":"https://pith.science/api/pith-number/V2ZLH2QYEO4HNOTUIO4NCK6DK7/graph.json","events_json":"https://pith.science/api/pith-number/V2ZLH2QYEO4HNOTUIO4NCK6DK7/events.json","paper":"https://pith.science/paper/V2ZLH2QY"},"agent_actions":{"view_html":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7","download_json":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7.json","view_paper":"https://pith.science/paper/V2ZLH2QY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.09137&json=true","fetch_graph":"https://pith.science/api/pith-number/V2ZLH2QYEO4HNOTUIO4NCK6DK7/graph.json","fetch_events":"https://pith.science/api/pith-number/V2ZLH2QYEO4HNOTUIO4NCK6DK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7/action/storage_attestation","attest_author":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7/action/author_attestation","sign_citation":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7/action/citation_signature","submit_replication":"https://pith.science/pith/V2ZLH2QYEO4HNOTUIO4NCK6DK7/action/replication_record"}},"created_at":"2026-05-18T00:17:18.555562+00:00","updated_at":"2026-05-18T00:17:18.555562+00:00"}