{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T7BJW2B7DE2LE6QRQAUFQ4GQCZ","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":"6a697a07c3393716daeebb4c840d0aee195701b80d20bb95af5c90fcf53e2870","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-06-17T10:42:51Z","title_canon_sha256":"5ba26b965e5a3c2dc094e732a7f66e14d995b942304b1b8a842ba3f51ac64bc7"},"schema_version":"1.0","source":{"id":"1106.3439","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3439","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3439v3","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3439","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"T7BJW2B7DE2L","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T7BJW2B7DE2LE6QR","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T7BJW2B7","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:6015bb32b43cd3562193af87a21fa5010e5e330209169f0102981952d3c0ec65","target":"graph","created_at":"2026-05-18T02:37:45Z","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":"We show that there exists a hyperbolic entire function of finite order of growth such that the hyperbolic dimension---that is, the Hausdorff dimension of the set of points in the Julia set of whose orbit is bounded---is equal to two. This is in contrast to the rational case, where the Julia set of a hyperbolic map must have Hausdorff dimension less than two, and to the case of all known explicit hyperbolic entire functions.\n  In order to obtain this example, we prove a general result on constructing entire functions in the Eremenko-Lyubich class with prescribed behavior near infinity, using Ca","authors_text":"Lasse Rempe-Gillen","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-06-17T10:42:51Z","title":"Hyperbolic entire functions with full hyperbolic dimension and approximation by Eremenko-Lyubich functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3439","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":"sha256:5d9438363da01020e25a88fa75c812153124b9bf3b1fc51e7a88d2b305297b78","target":"record","created_at":"2026-05-18T02:37:45Z","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":"6a697a07c3393716daeebb4c840d0aee195701b80d20bb95af5c90fcf53e2870","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-06-17T10:42:51Z","title_canon_sha256":"5ba26b965e5a3c2dc094e732a7f66e14d995b942304b1b8a842ba3f51ac64bc7"},"schema_version":"1.0","source":{"id":"1106.3439","kind":"arxiv","version":3}},"canonical_sha256":"9fc29b683f1934b27a1180285870d0166576e1bde3e6d5b3ab45de93ffda8366","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fc29b683f1934b27a1180285870d0166576e1bde3e6d5b3ab45de93ffda8366","first_computed_at":"2026-05-18T02:37:45.049426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:45.049426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0hNqEoCKvFVZmVswVnuAZXOIC93srytEaaFA6c7K9zHSKpW8144nwAWIgHMZV7avEHVWQuO20sWeQByQmc0+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:45.049892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3439","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d9438363da01020e25a88fa75c812153124b9bf3b1fc51e7a88d2b305297b78","sha256:6015bb32b43cd3562193af87a21fa5010e5e330209169f0102981952d3c0ec65"],"state_sha256":"54a38eacc36b7eef19cb76ec480af2306ff9fb6cf080347511b675c059ce59d4"}