{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DMVMREZ4JLDOBF3EBLSO5UKT2N","short_pith_number":"pith:DMVMREZ4","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"},"canonical_sha256":"1b2ac8933c4ac6e097640ae4eed153d365700c9ffc74f0c731669b7955a462a2","source":{"kind":"arxiv","id":"1908.06026","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06026","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06026v3","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06026","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"DMVMREZ4JLDO","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_16","alias_value":"DMVMREZ4JLDOBF3E","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_8","alias_value":"DMVMREZ4","created_at":"2026-07-05T01:15:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DMVMREZ4JLDOBF3EBLSO5UKT2N","target":"record","payload":{"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"},"canonical_sha256":"1b2ac8933c4ac6e097640ae4eed153d365700c9ffc74f0c731669b7955a462a2","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"},"source_kind":"arxiv","source_id":"1908.06026","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szLQO/C5RbwyREg1+h5LFsDaZqJ2J1DABBvT+PfH8P94Qh6Qq8QgueWSER8GpcjzxVaHNJGitxp++y8KYyJyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:30:52.069742Z"},"content_sha256":"61184a05efbea1db5be9943a1341923070c2283ad1b152b577f7cf71b915a540","schema_version":"1.0","event_id":"sha256:61184a05efbea1db5be9943a1341923070c2283ad1b152b577f7cf71b915a540"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DMVMREZ4JLDOBF3EBLSO5UKT2N","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kN44GxLQMIYgMpwfb1/sJKcxSh7KVkXgl7ld7Z83wrLdXhSd5aQakl0NupAXTtA1bPQTX9y941mCKk78kdT8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:30:52.070258Z"},"content_sha256":"ade3e0bd916e77fb205db55954341f2b3d6f57e0366aba46ab3acd95d32fed80","schema_version":"1.0","event_id":"sha256:ade3e0bd916e77fb205db55954341f2b3d6f57e0366aba46ab3acd95d32fed80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/bundle.json","state_url":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T08:30:52Z","links":{"resolver":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N","bundle":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/bundle.json","state":"https://pith.science/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMVMREZ4JLDOBF3EBLSO5UKT2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DMVMREZ4JLDOBF3EBLSO5UKT2N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d4c24dbb2a018891652704d9fc95cc294e5f7e6a5842f4633a05e60a226335a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-16T15:34:40Z","title_canon_sha256":"6c79b4924f0e59e9938026ca123b4ec24f1ea88166af78c048d6eac20c8c6ce4"},"schema_version":"1.0","source":{"id":"1908.06026","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06026","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06026v3","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06026","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"DMVMREZ4JLDO","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_16","alias_value":"DMVMREZ4JLDOBF3E","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_8","alias_value":"DMVMREZ4","created_at":"2026-07-05T01:15:55Z"}],"graph_snapshots":[{"event_id":"sha256:ade3e0bd916e77fb205db55954341f2b3d6f57e0366aba46ab3acd95d32fed80","target":"graph","created_at":"2026-07-05T01:15:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.06026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Luka Boc Thaler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-16T15:34:40Z","title":"Entire functions with prescribed singular values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06026","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:61184a05efbea1db5be9943a1341923070c2283ad1b152b577f7cf71b915a540","target":"record","created_at":"2026-07-05T01:15:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d4c24dbb2a018891652704d9fc95cc294e5f7e6a5842f4633a05e60a226335a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-16T15:34:40Z","title_canon_sha256":"6c79b4924f0e59e9938026ca123b4ec24f1ea88166af78c048d6eac20c8c6ce4"},"schema_version":"1.0","source":{"id":"1908.06026","kind":"arxiv","version":3}},"canonical_sha256":"1b2ac8933c4ac6e097640ae4eed153d365700c9ffc74f0c731669b7955a462a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b2ac8933c4ac6e097640ae4eed153d365700c9ffc74f0c731669b7955a462a2","first_computed_at":"2026-07-05T01:15:55.173779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:15:55.173779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rmuPxqUUNJOJg9ydFoILVnf6W9cV4NSzYoGS62TeYf4FssJgRNTLmsk9/mUhU7LuqioKKtRMfCT6suo/xkAaBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:15:55.174131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06026","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61184a05efbea1db5be9943a1341923070c2283ad1b152b577f7cf71b915a540","sha256:ade3e0bd916e77fb205db55954341f2b3d6f57e0366aba46ab3acd95d32fed80"],"state_sha256":"10b372e15850e466895ab6606d81ca8ef9cb03e3475bcefcdcbc76f7b051ee81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djkOwnFuGbBEBYON+mem3eNkUMyV55/7pE3ND9pHGz6rAdMrE9VswGlk5kcl5xpoAGP1zITl9id9KosLW+9YBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:30:52.075186Z","bundle_sha256":"c29f6a82fb134b42f0cdfc42098bc2750e412111589c4b4f9a1912b202e7aea2"}}