{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:6SWB6KBXXZNBB3R4F3PX2SVM33","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":"a5f031c0c75eb7e1309fd995e99c12464b449fb578fac9b3324ed13b9fcee9fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-28T16:14:46Z","title_canon_sha256":"28b5e65f157887f774280e0128186b465b57f1a09bef50a484002f3b7b1ec015"},"schema_version":"1.0","source":{"id":"2103.00546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.00546","created_at":"2026-07-05T02:19:06Z"},{"alias_kind":"arxiv_version","alias_value":"2103.00546v1","created_at":"2026-07-05T02:19:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.00546","created_at":"2026-07-05T02:19:06Z"},{"alias_kind":"pith_short_12","alias_value":"6SWB6KBXXZNB","created_at":"2026-07-05T02:19:06Z"},{"alias_kind":"pith_short_16","alias_value":"6SWB6KBXXZNBB3R4","created_at":"2026-07-05T02:19:06Z"},{"alias_kind":"pith_short_8","alias_value":"6SWB6KBX","created_at":"2026-07-05T02:19:06Z"}],"graph_snapshots":[{"event_id":"sha256:1e08ee4a0430dec38798c6f57a72df4be9bfb1168f9a389247160cbbfb94a98b","target":"graph","created_at":"2026-07-05T02:19:06Z","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/2103.00546/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the Diophantine properties of the orbits of a fixed point in its expansions under continuum many bases. More precisely, let $T_{\\beta}$ be the beta-transformation with base $\\beta>1$, $\\{x_{n}\\}_{n\\geq 1}$ be a sequence of real numbers in $[0,1]$ and $\\varphi\\colon \\mathbb{N}\\rightarrow (0,1]$ be a positive function. With a detailed analysis on the distribution of {\\em full cylinders} in the base space $\\{\\beta>1\\}$, it is shown that for any given $x\\in(0,1]$, for almost all or almost no bases $\\beta>1$, the orbit of $x$ under $T_{\\beta}$ can $\\varphi$-well approximate ","authors_text":"Baowei Wang, Fan Lv, Jun Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-28T16:14:46Z","title":"Diophantine analysis of the expansions of a fixed point under continuum many bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.00546","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:d01010a0b08507bcd386ab98fcea261adf5e9d131e2d8cb013676b430f089cb7","target":"record","created_at":"2026-07-05T02:19:06Z","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":"a5f031c0c75eb7e1309fd995e99c12464b449fb578fac9b3324ed13b9fcee9fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-28T16:14:46Z","title_canon_sha256":"28b5e65f157887f774280e0128186b465b57f1a09bef50a484002f3b7b1ec015"},"schema_version":"1.0","source":{"id":"2103.00546","kind":"arxiv","version":1}},"canonical_sha256":"f4ac1f2837be5a10ee3c2edf7d4aacdee3490227a999fe373d41c214071aaaab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4ac1f2837be5a10ee3c2edf7d4aacdee3490227a999fe373d41c214071aaaab","first_computed_at":"2026-07-05T02:19:06.784906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:19:06.784906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HPSlbyl8HmvyZ30wJjcre9kie/C3hD9QkLmuHPWnHQh3KDEVGmTESATpvr8B0EduNc6qWJLuFqwpDPwqEDGrAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:19:06.785323Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.00546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d01010a0b08507bcd386ab98fcea261adf5e9d131e2d8cb013676b430f089cb7","sha256:1e08ee4a0430dec38798c6f57a72df4be9bfb1168f9a389247160cbbfb94a98b"],"state_sha256":"b2eac47f0b0409c3026ba885bc54a422487d38d9d3f819684b13ae0303b22043"}