{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q57OHUALLZPQVN2NOXGRZ3EAJQ","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":"6b162658f46f01b112db4d239f7bdbdaa559d020eecda7e8f777104c8d2cd424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-16T06:16:55Z","title_canon_sha256":"38072c4ddf01ce67dcb43d4a9855ed11f041a169f1465e69bba2024f399d896a"},"schema_version":"1.0","source":{"id":"1301.3595","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3595","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3595v2","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3595","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"pith_short_12","alias_value":"Q57OHUALLZPQ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q57OHUALLZPQVN2N","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q57OHUAL","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:596e3833bac3f85001d684b6777311fdf39aeb36106a5f9682452e99e3b603c6","target":"graph","created_at":"2026-05-18T03:30:27Z","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 consider the distribution of the orbits of the number 1 under the $\\beta$-transformations $T_\\beta$ as $\\beta$ varies. Mainly, the size of the set of $\\beta>1$ for which a given point can be well approximated by the orbit of 1 is measured by its Hausdorff dimension. That is, the dimension of the following set $$ E\\big({\\ell_n}_{n\\ge 1}, x_0\\big)=\\Big{\\beta>1: |T^n_{\\beta}1-x_0|<\\beta^{-\\ell_n}, {for infinitely many} n\\in \\N\\Big} $$ is determined, where $x_0$ is a given point in $[0,1]$ and ${\\ell_n}_{n\\ge 1}$ is a sequence of integers tending to infinity as $n\\to \\infty$. For the proof of t","authors_text":"Baowei Wang, Bing Li, Jun Wu, Tomas Persson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-16T06:16:55Z","title":"Diophantine approximation of the orbit of 1 in the dynamical system of bete expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3595","kind":"arxiv","version":2},"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:b6ea6b1bdb749285395447685c508e4495f6fb8c46a481d25d063002e80bdb6a","target":"record","created_at":"2026-05-18T03:30:27Z","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":"6b162658f46f01b112db4d239f7bdbdaa559d020eecda7e8f777104c8d2cd424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-16T06:16:55Z","title_canon_sha256":"38072c4ddf01ce67dcb43d4a9855ed11f041a169f1465e69bba2024f399d896a"},"schema_version":"1.0","source":{"id":"1301.3595","kind":"arxiv","version":2}},"canonical_sha256":"877ee3d00b5e5f0ab74d75cd1cec804c198dbd5f306dcba867378680f3537fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"877ee3d00b5e5f0ab74d75cd1cec804c198dbd5f306dcba867378680f3537fd4","first_computed_at":"2026-05-18T03:30:27.528341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:27.528341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X2me4+bQqsrNo0G5NKTSZlAbdbmMz7b6G3SccZZgMI2jBAGEYsEXOmsiENpFJiXb1DLp4+180N33Vqp1x8GzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:27.529313Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3595","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6ea6b1bdb749285395447685c508e4495f6fb8c46a481d25d063002e80bdb6a","sha256:596e3833bac3f85001d684b6777311fdf39aeb36106a5f9682452e99e3b603c6"],"state_sha256":"3ad602ae9de9481619610a058431758780bd6597af7b301803b136842da2de68"}