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This is the sequence of non-negative integers $s_0s_1...$ defined by \\[ f^n(z)\\in A_{s_n}(R),\\;\\;\\text{for}n\\ge 0, \\] where $A_0(R)=\\{z:|z|<R\\}$ and \\[ A_n(R)=\\{z:M^{n-1}(R)\\le |z|<M^n(R)\\},\\;\\;n\\ge 1. \\] Here $M(r)$ is the maximum modulus of $f$ and $R>0$ is so large that $M(r)>r$, for $r\\ge R$.\n  We consider the different types of annular itineraries that can occur for any transcendental entire fun"},"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":"1301.1328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-07T20:38:36Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"1c462a11e039456bb5ab18f7fe301fa5ff472dffb268abfb510a6313d17c66d9","abstract_canon_sha256":"b755608976d1810f97c1f1451d2be35c8865ce9c281c7d10b90275fcf0300a35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:06.171552Z","signature_b64":"gZreG30X5lPiPtV23h2UMw8HNLi+1bGHfUd2Kg67FTRFHyXoroVz2RnuYsNzeJXPEaT6uamDp9y5EwJR4nW5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"985e6e45d06e5ba1a553c6e9dc02cb882aa985371f692c02c2f48db8588a5cf3","last_reissued_at":"2026-05-18T03:37:06.170704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:06.170704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Annular itineraries for entire functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Gwyneth M. 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