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A $d$-dimensional vector $x=(x_1,\\dots,x_d)\\in\\mathbb{R}^d$ is said to be $w$-singular if for every $\\epsilon>0$ there exists $T_0>1$ such that for all $T>T_0$ the system of inequalities \\[ \\max_{1\\leq i\\leq d}|qx_i - p_i|^{\\frac{1}{w_i}} < \\frac{\\epsilon}{T} \\quad\\text{and}\\quad 0<q<T \\] have an integer solution $(\\mathbf{p},q)=(p_1,\\dots,p_d,q)\\in \\mathbb{Z}^d \\times \\mathbb{Z}$. We prove that the Hausdorff dimension of the set of $w$-singular vectors in $\\mathbb{R}^d$ is","authors_text":"Jaemin Park, Taehyeong Kim","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-07-16T13:35:30Z","title":"On a lower bound of Hausdorff dimension of weighted singular vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.07944","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":"sha256:948787364b921bb8990b5e82f12853d982ce7a1f7ec7c9cec017acbd0989e25f","target":"record","created_at":"2026-07-05T08:05:46Z","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":"f27b201dac491124f84fd8e731fd90590b786a5e5551d3ae72c0155dce1d97b7","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-07-16T13:35:30Z","title_canon_sha256":"3df10875821871063c4ee2953600475ea2a0efc68ebe7b0d50b637e3fedbbd58"},"schema_version":"1.0","source":{"id":"2207.07944","kind":"arxiv","version":2}},"canonical_sha256":"0b2fcef4be852644726dc79e2af191ae109e1e4726cc37502ec25c1888fa2bd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b2fcef4be852644726dc79e2af191ae109e1e4726cc37502ec25c1888fa2bd9","first_computed_at":"2026-07-05T08:05:46.774138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:05:46.774138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a44chk+rQN7bbY8ALhzT9FdzCoHdDKGXofVW4Ivbtx1vwG5ScrZo+PXIgme9TRbOJaO1gPm0K8C59015n8BMCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:05:46.774517Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.07944","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:948787364b921bb8990b5e82f12853d982ce7a1f7ec7c9cec017acbd0989e25f","sha256:311d27d07327c185208bf6ce52001b7555cc87c77b66376aad52ff58df6e3ec5"],"state_sha256":"c3d93a1e125180d9a9caa46b6355258cda5f2dd4aa645350c48f1ff361261d3f"}