{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CFC2AMUCBMLBHPTMVPJKO6LO2N","short_pith_number":"pith:CFC2AMUC","schema_version":"1.0","canonical_sha256":"1145a032820b1613be6cabd2a7796ed34221e79dd5c7354b8b435f39422cd0dc","source":{"kind":"arxiv","id":"1304.7502","version":2},"attestation_state":"computed","paper":{"title":"Guiding Isotopies and Holomorphic Motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Frederick. P. Gardiner, Yunping Jiang","submitted_at":"2013-04-28T19:15:03Z","abstract_excerpt":"We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion of a finite subset $E$ of a Riemann surface $Y$ parameterized by a point $t$ in a pointed hyperbolic surface $(X, t_{0})$. If a holomorphic motion from $E$ to $E_{t}$ in $Y$ has a guiding quasiconformal isotopy, then there is a holomorphic extension to any new point $p$ in $Y-E$ that follows the guiding isotopy. The proof gives a canonical way to replace a quasiconformal motion of the $(n+1)^{th}$ point by a holomorphic motion while leaving unchanged the given 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":"1304.7502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-28T19:15:03Z","cross_cats_sorted":[],"title_canon_sha256":"db1246bee3b172be48f1598e9d6fb1011d16eaef94bf3d426f7a9c7553f74104","abstract_canon_sha256":"d05fb598e8780a7f09d95eb88f96d1f9801b9a492fed80e6ffdf88da09fd502c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:46.580741Z","signature_b64":"ODyUDIK9CQ1jjF1Pu50Dgyi8htoNm/PwkgxKyAamUDejrPoBW5m8vUTs7RO9nsGGV6KTHxl7jkoZlENiOC+ECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1145a032820b1613be6cabd2a7796ed34221e79dd5c7354b8b435f39422cd0dc","last_reissued_at":"2026-05-18T03:01:46.580179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:46.580179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Guiding Isotopies and Holomorphic Motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Frederick. P. Gardiner, Yunping Jiang","submitted_at":"2013-04-28T19:15:03Z","abstract_excerpt":"We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion of a finite subset $E$ of a Riemann surface $Y$ parameterized by a point $t$ in a pointed hyperbolic surface $(X, t_{0})$. If a holomorphic motion from $E$ to $E_{t}$ in $Y$ has a guiding quasiconformal isotopy, then there is a holomorphic extension to any new point $p$ in $Y-E$ that follows the guiding isotopy. The proof gives a canonical way to replace a quasiconformal motion of the $(n+1)^{th}$ point by a holomorphic motion while leaving unchanged the given holomorphic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7502","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":"1304.7502","created_at":"2026-05-18T03:01:46.580259+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7502v2","created_at":"2026-05-18T03:01:46.580259+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7502","created_at":"2026-05-18T03:01:46.580259+00:00"},{"alias_kind":"pith_short_12","alias_value":"CFC2AMUCBMLB","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CFC2AMUCBMLBHPTM","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CFC2AMUC","created_at":"2026-05-18T12:27:40.988391+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/CFC2AMUCBMLBHPTMVPJKO6LO2N","json":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N.json","graph_json":"https://pith.science/api/pith-number/CFC2AMUCBMLBHPTMVPJKO6LO2N/graph.json","events_json":"https://pith.science/api/pith-number/CFC2AMUCBMLBHPTMVPJKO6LO2N/events.json","paper":"https://pith.science/paper/CFC2AMUC"},"agent_actions":{"view_html":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N","download_json":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N.json","view_paper":"https://pith.science/paper/CFC2AMUC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7502&json=true","fetch_graph":"https://pith.science/api/pith-number/CFC2AMUCBMLBHPTMVPJKO6LO2N/graph.json","fetch_events":"https://pith.science/api/pith-number/CFC2AMUCBMLBHPTMVPJKO6LO2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N/action/storage_attestation","attest_author":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N/action/author_attestation","sign_citation":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N/action/citation_signature","submit_replication":"https://pith.science/pith/CFC2AMUCBMLBHPTMVPJKO6LO2N/action/replication_record"}},"created_at":"2026-05-18T03:01:46.580259+00:00","updated_at":"2026-05-18T03:01:46.580259+00:00"}