{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q5TEPZIIMLNUUDHPQYMQRXMDRV","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":"2ffc01f00e5a03da3e2a691c7cb1000be48b9084b9aa31b378a60166aba69aa1","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-30T12:12:17Z","title_canon_sha256":"50689ad24c7fa68a766fa12799df29ebbb35db67bd04fe84318d1aab14c6e913"},"schema_version":"1.0","source":{"id":"1801.00124","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00124","created_at":"2026-07-05T00:27:13Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00124v1","created_at":"2026-07-05T00:27:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00124","created_at":"2026-07-05T00:27:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q5TEPZIIMLNU","created_at":"2026-07-05T00:27:13Z"},{"alias_kind":"pith_short_16","alias_value":"Q5TEPZIIMLNUUDHP","created_at":"2026-07-05T00:27:13Z"},{"alias_kind":"pith_short_8","alias_value":"Q5TEPZII","created_at":"2026-07-05T00:27:13Z"}],"graph_snapshots":[{"event_id":"sha256:48459dac777705611d3c217d66cbc6df3062093e1c980e68ea92b63c4b2ee7c1","target":"graph","created_at":"2026-07-05T00:27:13Z","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/1801.00124/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the iteration of transcendental self-maps of $\\mathbb{C}^*:=\\mathbb{C}\\setminus \\{0\\}$, that is, holomorphic functions $f:\\mathbb{C}^*\\to\\mathbb{C}^*$ for which both zero and infinity are essential singularities. We use approximation theory to construct functions in this class with escaping Fatou components, both wandering domains and Baker domains, that accumulate to $\\{0,\\infty\\}$ in any possible way under iteration. We also give the first explicit examples of transcendental self-maps of $\\mathbb{C}^*$ with Baker domains and with wandering domains. In doing so, we developed a suffic","authors_text":"David Mart\\'i-Pete","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-30T12:12:17Z","title":"Escaping Fatou components of transcendental self-maps of the punctured plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00124","kind":"arxiv","version":1},"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":"sha256:296ced2e4bba7d58a7e45a242cfd314060f0a70c6aec47252fa80939eb8945fc","target":"record","created_at":"2026-07-05T00:27:13Z","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":"2ffc01f00e5a03da3e2a691c7cb1000be48b9084b9aa31b378a60166aba69aa1","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-30T12:12:17Z","title_canon_sha256":"50689ad24c7fa68a766fa12799df29ebbb35db67bd04fe84318d1aab14c6e913"},"schema_version":"1.0","source":{"id":"1801.00124","kind":"arxiv","version":1}},"canonical_sha256":"876647e50862db4a0cef861908dd838d7cdc8ccd06f4668f4843578e25f07a4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"876647e50862db4a0cef861908dd838d7cdc8ccd06f4668f4843578e25f07a4f","first_computed_at":"2026-07-05T00:27:13.263056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:27:13.263056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IurIjRikY5srrB1+qqs05FSGDxC9Wr280cWpK412YPoQHaekh2/J13yWKoQvv9C1HajNY+KPcgZFfieBpSeQDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:27:13.263475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00124","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:296ced2e4bba7d58a7e45a242cfd314060f0a70c6aec47252fa80939eb8945fc","sha256:48459dac777705611d3c217d66cbc6df3062093e1c980e68ea92b63c4b2ee7c1"],"state_sha256":"92a4eff5fbde125ff8b1d03d64c9aa6109809d446b940cbd0b2e2f7f4dfa676a"}