{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GYLHNK64ZJXW4JUKMCCC6LJEXH","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":"12190790d648ff670a9735c47c0395cc8d182f42154f4998002082157f0f7826","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-22T16:19:45Z","title_canon_sha256":"505faf032625373a3976485d7453a96a9b401778f0c663625ffb096b9c34e96f"},"schema_version":"1.0","source":{"id":"1201.4568","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4568","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4568v2","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4568","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"GYLHNK64ZJXW","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GYLHNK64ZJXW4JUK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GYLHNK64","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:9438ee93a7c694756b68ad3819e5726761ad1cb7db5f54108896a0f8c5161696","target":"graph","created_at":"2026-05-18T03:07:12Z","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 discuss the shrinking target property of irrational rotations. We obtain the condition of an irrational $\\theta$ and monotone increasing $\\varphi(n)$ such that $$ \\liminf_{n \\to \\infty} n \\varphi (n) \\| n\\theta - s \\| = 0 \\text{ for almost every } s. $$ We also consider the class of irrationals for which the limit inferior is 0 for every monotone increasing $\\varphi(n)$ such that $\\sum_n 1/(n\\varphi(n))$ diverges.","authors_text":"Dong Han Kim","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-22T16:19:45Z","title":"On the refined shrinking target property of rotations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4568","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:fc98c227485f922736dd6d0b47c47f59a5039bcb4ac9763684e8e552bb0d6456","target":"record","created_at":"2026-05-18T03:07:12Z","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":"12190790d648ff670a9735c47c0395cc8d182f42154f4998002082157f0f7826","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-22T16:19:45Z","title_canon_sha256":"505faf032625373a3976485d7453a96a9b401778f0c663625ffb096b9c34e96f"},"schema_version":"1.0","source":{"id":"1201.4568","kind":"arxiv","version":2}},"canonical_sha256":"361676abdcca6f6e268a60842f2d24b9de7e6dd1b8e3a99b05580c8e902602ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"361676abdcca6f6e268a60842f2d24b9de7e6dd1b8e3a99b05580c8e902602ae","first_computed_at":"2026-05-18T03:07:12.387637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:12.387637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I59Wy5IuxcU6uJ/DZhrQmKnt8xd/ratmqa/Eu34ymZmps7QkGughKmk29EbajUQ1mgx+l0xie9KS1/FnRd7wAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:12.388229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4568","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc98c227485f922736dd6d0b47c47f59a5039bcb4ac9763684e8e552bb0d6456","sha256:9438ee93a7c694756b68ad3819e5726761ad1cb7db5f54108896a0f8c5161696"],"state_sha256":"99c7dfe8251b38c7f708eefbd8bc6ad0e7531dbe64f7f0bb2270ae7df3eb97f3"}