{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JGXNGSQH3YJRJ7BWW734WVL4NC","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":"6bafd4b2af259ce2bec14c6ba27c5bea6e9514e7b94595842a8bae2ea8958610","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-10T17:16:38Z","title_canon_sha256":"fa7a57bda30b093d4bab476555567c104d471ab8e5c348c1763fe2bfa9efdd05"},"schema_version":"1.0","source":{"id":"1301.2193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2193","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2193v1","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2193","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"JGXNGSQH3YJR","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JGXNGSQH3YJRJ7BW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JGXNGSQH","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:c48a2de614f2ed7f81b6e12e0bae4e163384f63a8b5d9f2c59f197cbdcf6a6ac","target":"graph","created_at":"2026-05-18T03:36:47Z","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"},"paper":{"abstract_excerpt":"Let $f$ be a transcendental entire function. The fast escaping set $A(f)$, various regularity conditions on the growth of the maximum modulus of $f$, and also, more recently, the quite fast escaping set $Q(f)$ have all been used to make progress on fundamental questions concerning the iteration of $f$. In this paper we establish new relationships between these three concepts.\n  We prove that a certain weak regularity condition is necessary and sufficient for $Q(f)=A(f)$ and give examples of functions for which $Q(f)\\neq A(f)$.\n  We also apply a result of Beurling that relates the size of the m","authors_text":"Gwyneth M. Stallard, Philip J. Rippon","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-10T17:16:38Z","title":"Regularity and fast escaping points of entire functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2193","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:b6fc2a1b2ef5a7028fbdd24fb9f03fa0e3169e23f890a74c795a847984d075ad","target":"record","created_at":"2026-05-18T03:36:47Z","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":"6bafd4b2af259ce2bec14c6ba27c5bea6e9514e7b94595842a8bae2ea8958610","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-10T17:16:38Z","title_canon_sha256":"fa7a57bda30b093d4bab476555567c104d471ab8e5c348c1763fe2bfa9efdd05"},"schema_version":"1.0","source":{"id":"1301.2193","kind":"arxiv","version":1}},"canonical_sha256":"49aed34a07de1314fc36b7f7cb557c68a982d3268cbda4ab1ac48ef220be53fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49aed34a07de1314fc36b7f7cb557c68a982d3268cbda4ab1ac48ef220be53fc","first_computed_at":"2026-05-18T03:36:47.237550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:47.237550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xuv+npeIUP4/gz9qA9wAy+79CDu0SLhIXWAf5LHFuh5DCCHjyKjRgw1eTbm9sCE6x4MBX+NFAgdTDSPnhJ9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:47.238207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6fc2a1b2ef5a7028fbdd24fb9f03fa0e3169e23f890a74c795a847984d075ad","sha256:c48a2de614f2ed7f81b6e12e0bae4e163384f63a8b5d9f2c59f197cbdcf6a6ac"],"state_sha256":"4a7943c5d7384c5156eb07e86e139943dd518c4a16c5ac9c5ae8afb358ed2ed7"}