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This new class is closed under the composition and its is dense in the space of all non-vanishing entire functions. We prove that every closed set $V\\subset \\mathbb{C}$ containing the origin and at least one more point is the set of singular values of some locally univalent function in $\\mathcal{E}$, hence t"},"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":"1908.06026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-16T15:34:40Z","cross_cats_sorted":[],"title_canon_sha256":"6c79b4924f0e59e9938026ca123b4ec24f1ea88166af78c048d6eac20c8c6ce4","abstract_canon_sha256":"d4c24dbb2a018891652704d9fc95cc294e5f7e6a5842f4633a05e60a226335a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:15:55.174131Z","signature_b64":"rmuPxqUUNJOJg9ydFoILVnf6W9cV4NSzYoGS62TeYf4FssJgRNTLmsk9/mUhU7LuqioKKtRMfCT6suo/xkAaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b2ac8933c4ac6e097640ae4eed153d365700c9ffc74f0c731669b7955a462a2","last_reissued_at":"2026-07-05T01:15:55.173779Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:15:55.173779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entire functions with prescribed singular values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Luka Boc Thaler","submitted_at":"2019-08-16T15:34:40Z","abstract_excerpt":"We introduce a new class of entire functions $\\mathcal{E}$ which consists of all $F_0\\in\\mathcal{O}(\\mathbb{C})$ for which there exists a sequence $(F_n)\\in \\mathcal{O}(\\mathbb{C})$ and a sequence $(\\lambda_n)\\in\\mathbb{C}$ satisfying $F_n(z)=\\lambda_{n+1}e^{F_{n+1}(z)}$ for all $n\\geq 0$. This new class is closed under the composition and its is dense in the space of all non-vanishing entire functions. We prove that every closed set $V\\subset \\mathbb{C}$ containing the origin and at least one more point is the set of singular values of some locally univalent function in $\\mathcal{E}$, hence t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06026","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.06026","created_at":"2026-07-05T01:15:55.173833+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06026v3","created_at":"2026-07-05T01:15:55.173833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06026","created_at":"2026-07-05T01:15:55.173833+00:00"},{"alias_kind":"pith_short_12","alias_value":"DMVMREZ4JLDO","created_at":"2026-07-05T01:15:55.173833+00:00"},{"alias_kind":"pith_short_16","alias_value":"DMVMREZ4JLDOBF3E","created_at":"2026-07-05T01:15:55.173833+00:00"},{"alias_kind":"pith_short_8","alias_value":"DMVMREZ4","created_at":"2026-07-05T01:15:55.173833+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/DMVMREZ4JLDOBF3EBLSO5UKT2N","json":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N.json","graph_json":"https://pith.science/api/pith-number/DMVMREZ4JLDOBF3EBLSO5UKT2N/graph.json","events_json":"https://pith.science/api/pith-number/DMVMREZ4JLDOBF3EBLSO5UKT2N/events.json","paper":"https://pith.science/paper/DMVMREZ4"},"agent_actions":{"view_html":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N","download_json":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N.json","view_paper":"https://pith.science/paper/DMVMREZ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06026&json=true","fetch_graph":"https://pith.science/api/pith-number/DMVMREZ4JLDOBF3EBLSO5UKT2N/graph.json","fetch_events":"https://pith.science/api/pith-number/DMVMREZ4JLDOBF3EBLSO5UKT2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/action/storage_attestation","attest_author":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/action/author_attestation","sign_citation":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/action/citation_signature","submit_replication":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/action/replication_record"}},"created_at":"2026-07-05T01:15:55.173833+00:00","updated_at":"2026-07-05T01:15:55.173833+00:00"}