{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:HR7U65XBYCD3J5PACPZODKXTWD","short_pith_number":"pith:HR7U65XB","schema_version":"1.0","canonical_sha256":"3c7f4f76e1c087b4f5e013f2e1aaf3b0de2f954f80614a903e764f55dd8586be","source":{"kind":"arxiv","id":"0705.1851","version":2},"attestation_state":"computed","paper":{"title":"The Riemann Mapping Theorem for semianalytic domains and o-minimality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tobias Kaiser","submitted_at":"2007-05-14T12:21:52Z","abstract_excerpt":"We consider the Riemann Mapping Theorem in the case of a bounded simply connected and semianalytic domain. We show that the germ at 0 of the Riemann map (i.e. biholomorphic map) from the upper half plane to such a domain can be realized in a certain quasianalytic class if the angle of the boundary at the point to which 0 is mapped, is greater than 0. This quasianalytic class was introduced and used by Ilyashenko in his work on Hilbert's 16th problem. With this result we can prove that the Riemann map from a bounded simply connected semianalytic domain onto the unit ball is definable in an o-mi"},"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":"0705.1851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2007-05-14T12:21:52Z","cross_cats_sorted":[],"title_canon_sha256":"acdaeca54e540fa041e243a70d51a588c42f4a824f846f3147ee49af23cbc595","abstract_canon_sha256":"33040d4132586240a5bfb17060ac5b54172ec11e3be34285e027045b410ead5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:12.725699Z","signature_b64":"xnFhDNcBEMawdeKjZuqp847djZut/CgNK3Uvznad1zkZQJD5novmcbqPKmy4jx5mFHmB4jtBmz9ZA8/mOznYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c7f4f76e1c087b4f5e013f2e1aaf3b0de2f954f80614a903e764f55dd8586be","last_reissued_at":"2026-05-18T02:58:12.724861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:12.724861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Riemann Mapping Theorem for semianalytic domains and o-minimality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tobias Kaiser","submitted_at":"2007-05-14T12:21:52Z","abstract_excerpt":"We consider the Riemann Mapping Theorem in the case of a bounded simply connected and semianalytic domain. We show that the germ at 0 of the Riemann map (i.e. biholomorphic map) from the upper half plane to such a domain can be realized in a certain quasianalytic class if the angle of the boundary at the point to which 0 is mapped, is greater than 0. This quasianalytic class was introduced and used by Ilyashenko in his work on Hilbert's 16th problem. With this result we can prove that the Riemann map from a bounded simply connected semianalytic domain onto the unit ball is definable in an o-mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.1851","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":"0705.1851","created_at":"2026-05-18T02:58:12.725008+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.1851v2","created_at":"2026-05-18T02:58:12.725008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.1851","created_at":"2026-05-18T02:58:12.725008+00:00"},{"alias_kind":"pith_short_12","alias_value":"HR7U65XBYCD3","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"HR7U65XBYCD3J5PA","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"HR7U65XB","created_at":"2026-05-18T12:25:55.427421+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/HR7U65XBYCD3J5PACPZODKXTWD","json":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD.json","graph_json":"https://pith.science/api/pith-number/HR7U65XBYCD3J5PACPZODKXTWD/graph.json","events_json":"https://pith.science/api/pith-number/HR7U65XBYCD3J5PACPZODKXTWD/events.json","paper":"https://pith.science/paper/HR7U65XB"},"agent_actions":{"view_html":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD","download_json":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD.json","view_paper":"https://pith.science/paper/HR7U65XB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.1851&json=true","fetch_graph":"https://pith.science/api/pith-number/HR7U65XBYCD3J5PACPZODKXTWD/graph.json","fetch_events":"https://pith.science/api/pith-number/HR7U65XBYCD3J5PACPZODKXTWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD/action/storage_attestation","attest_author":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD/action/author_attestation","sign_citation":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD/action/citation_signature","submit_replication":"https://pith.science/pith/HR7U65XBYCD3J5PACPZODKXTWD/action/replication_record"}},"created_at":"2026-05-18T02:58:12.725008+00:00","updated_at":"2026-05-18T02:58:12.725008+00:00"}