{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HREAFX3WA7GUFG3KV5RBOZBHYZ","short_pith_number":"pith:HREAFX3W","schema_version":"1.0","canonical_sha256":"3c4802df7607cd429b6aaf62176427c64497b40aa654376c2006ada2d3efd7e9","source":{"kind":"arxiv","id":"1003.3947","version":1},"attestation_state":"computed","paper":{"title":"Carrots for dessert","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carsten Lunde Petersen, Pascale Roesch","submitted_at":"2010-03-20T19:35:02Z","abstract_excerpt":"Carrots for dessert is the title of a section of the paper `On polynomial-like mappings' by Douady and Hubbard. In that section the authors define a notion of dyadic carrot fields of the Mandelbrot set M and more generally for Mandelbrot like families. They remark that such carrots are small when the dyadic denominator is large, but they do not even try to prove a precise such statement. In this paper we formulate and prove a precise statement of asymptotic shrinking of dyadic Carrot-fields around M. The same proof carries readily over to show that the dyadic decorations of copies M' of the Ma"},"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":"1003.3947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-20T19:35:02Z","cross_cats_sorted":[],"title_canon_sha256":"9f27a5490305818f90ddf92f59ed174de6f6e52f9ff6aaad88d234f21d3c0feb","abstract_canon_sha256":"7e53739fc75fa617da1edf157ee50ca2d84e2ac64347eb832ba5bff2c3c849e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:00.743255Z","signature_b64":"53bXVAuegh7X02RNWqysw2RP4yn4uqwUP8U0kdcObj8uKc1Tnf1YxzlK0OqcH6tHku6ZGr/fMuCd6qlLsCf2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c4802df7607cd429b6aaf62176427c64497b40aa654376c2006ada2d3efd7e9","last_reissued_at":"2026-05-18T01:19:00.742871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:00.742871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Carrots for dessert","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carsten Lunde Petersen, Pascale Roesch","submitted_at":"2010-03-20T19:35:02Z","abstract_excerpt":"Carrots for dessert is the title of a section of the paper `On polynomial-like mappings' by Douady and Hubbard. In that section the authors define a notion of dyadic carrot fields of the Mandelbrot set M and more generally for Mandelbrot like families. They remark that such carrots are small when the dyadic denominator is large, but they do not even try to prove a precise such statement. In this paper we formulate and prove a precise statement of asymptotic shrinking of dyadic Carrot-fields around M. The same proof carries readily over to show that the dyadic decorations of copies M' of the Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3947","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":"1003.3947","created_at":"2026-05-18T01:19:00.742944+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.3947v1","created_at":"2026-05-18T01:19:00.742944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3947","created_at":"2026-05-18T01:19:00.742944+00:00"},{"alias_kind":"pith_short_12","alias_value":"HREAFX3WA7GU","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HREAFX3WA7GUFG3K","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HREAFX3W","created_at":"2026-05-18T12:26:07.630475+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/HREAFX3WA7GUFG3KV5RBOZBHYZ","json":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ.json","graph_json":"https://pith.science/api/pith-number/HREAFX3WA7GUFG3KV5RBOZBHYZ/graph.json","events_json":"https://pith.science/api/pith-number/HREAFX3WA7GUFG3KV5RBOZBHYZ/events.json","paper":"https://pith.science/paper/HREAFX3W"},"agent_actions":{"view_html":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ","download_json":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ.json","view_paper":"https://pith.science/paper/HREAFX3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.3947&json=true","fetch_graph":"https://pith.science/api/pith-number/HREAFX3WA7GUFG3KV5RBOZBHYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/HREAFX3WA7GUFG3KV5RBOZBHYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ/action/storage_attestation","attest_author":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ/action/author_attestation","sign_citation":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ/action/citation_signature","submit_replication":"https://pith.science/pith/HREAFX3WA7GUFG3KV5RBOZBHYZ/action/replication_record"}},"created_at":"2026-05-18T01:19:00.742944+00:00","updated_at":"2026-05-18T01:19:00.742944+00:00"}