{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:CJSQI5LZWDLG5ZZFCXGICCEJ6M","short_pith_number":"pith:CJSQI5LZ","schema_version":"1.0","canonical_sha256":"1265047579b0d66ee72515cc810889f30da8dcfb0a1473ab4edb754b58a66c3c","source":{"kind":"arxiv","id":"math/0206054","version":1},"attestation_state":"computed","paper":{"title":"Spinning deformations of rational maps","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Kevin M. Pilgrim, Tan Lei","submitted_at":"2002-06-06T15:10:11Z","abstract_excerpt":"We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges to infinity in the moduli space of rational maps of a fixed degree. When the limit exists, it has either a parabolic fixed point, or a pre-periodic critical point in the Julia set, depending on the combinatorics of the data defining the deformation. The proofs are soft and rely on two ingredients: the construction of a Riemann surface containing the closure o"},"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":"math/0206054","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2002-06-06T15:10:11Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"1ee2ae555b80ed5f6daac356fbd075795812622a7fdac796c96b126a99b66a65","abstract_canon_sha256":"912cfc0d4b2919222b9ae9bc185d3d7eb5f8bccb882989fae15dedbe2ee21d11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.529533Z","signature_b64":"sGW1kSft1ZUwSPBFaL/vwyH5gNNsvIB1r4Js2+rKbzn5HiAuVwEoo0RMukfVccm1xGD/rM8wXBxfZPB9P/CqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1265047579b0d66ee72515cc810889f30da8dcfb0a1473ab4edb754b58a66c3c","last_reissued_at":"2026-05-18T01:05:29.529081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.529081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spinning deformations of rational maps","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Kevin M. Pilgrim, Tan Lei","submitted_at":"2002-06-06T15:10:11Z","abstract_excerpt":"We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges to infinity in the moduli space of rational maps of a fixed degree. When the limit exists, it has either a parabolic fixed point, or a pre-periodic critical point in the Julia set, depending on the combinatorics of the data defining the deformation. The proofs are soft and rely on two ingredients: the construction of a Riemann surface containing the closure o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206054","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":"math/0206054","created_at":"2026-05-18T01:05:29.529145+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0206054v1","created_at":"2026-05-18T01:05:29.529145+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0206054","created_at":"2026-05-18T01:05:29.529145+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJSQI5LZWDLG","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJSQI5LZWDLG5ZZF","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJSQI5LZ","created_at":"2026-05-18T12:25:50.845339+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/CJSQI5LZWDLG5ZZFCXGICCEJ6M","json":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M.json","graph_json":"https://pith.science/api/pith-number/CJSQI5LZWDLG5ZZFCXGICCEJ6M/graph.json","events_json":"https://pith.science/api/pith-number/CJSQI5LZWDLG5ZZFCXGICCEJ6M/events.json","paper":"https://pith.science/paper/CJSQI5LZ"},"agent_actions":{"view_html":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M","download_json":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M.json","view_paper":"https://pith.science/paper/CJSQI5LZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0206054&json=true","fetch_graph":"https://pith.science/api/pith-number/CJSQI5LZWDLG5ZZFCXGICCEJ6M/graph.json","fetch_events":"https://pith.science/api/pith-number/CJSQI5LZWDLG5ZZFCXGICCEJ6M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M/action/storage_attestation","attest_author":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M/action/author_attestation","sign_citation":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M/action/citation_signature","submit_replication":"https://pith.science/pith/CJSQI5LZWDLG5ZZFCXGICCEJ6M/action/replication_record"}},"created_at":"2026-05-18T01:05:29.529145+00:00","updated_at":"2026-05-18T01:05:29.529145+00:00"}