{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:BMX455F6QUTEI4TNY6PCV4MRVY","short_pith_number":"pith:BMX455F6","schema_version":"1.0","canonical_sha256":"0b2fcef4be852644726dc79e2af191ae109e1e4726cc37502ec25c1888fa2bd9","source":{"kind":"arxiv","id":"2207.07944","version":2},"attestation_state":"computed","paper":{"title":"On a lower bound of Hausdorff dimension of weighted singular vectors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Jaemin Park, Taehyeong Kim","submitted_at":"2022-07-16T13:35:30Z","abstract_excerpt":"Let $w=(w_1,\\dots,w_d)$ be a $d$-tuple of positive real numbers such that $\\sum_{i}w_i =1$ and $w_1\\geq \\cdots \\geq w_d$. 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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2207.07944","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-07-16T13:35:30Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3df10875821871063c4ee2953600475ea2a0efc68ebe7b0d50b637e3fedbbd58","abstract_canon_sha256":"f27b201dac491124f84fd8e731fd90590b786a5e5551d3ae72c0155dce1d97b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:05:46.774517Z","signature_b64":"a44chk+rQN7bbY8ALhzT9FdzCoHdDKGXofVW4Ivbtx1vwG5ScrZo+PXIgme9TRbOJaO1gPm0K8C59015n8BMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b2fcef4be852644726dc79e2af191ae109e1e4726cc37502ec25c1888fa2bd9","last_reissued_at":"2026-07-05T08:05:46.774138Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:05:46.774138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a lower bound of Hausdorff dimension of weighted singular vectors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Jaemin Park, Taehyeong Kim","submitted_at":"2022-07-16T13:35:30Z","abstract_excerpt":"Let $w=(w_1,\\dots,w_d)$ be a $d$-tuple of positive real numbers such that $\\sum_{i}w_i =1$ and $w_1\\geq \\cdots \\geq w_d$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.07944","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.07944/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2207.07944","created_at":"2026-07-05T08:05:46.774192+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.07944v2","created_at":"2026-07-05T08:05:46.774192+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.07944","created_at":"2026-07-05T08:05:46.774192+00:00"},{"alias_kind":"pith_short_12","alias_value":"BMX455F6QUTE","created_at":"2026-07-05T08:05:46.774192+00:00"},{"alias_kind":"pith_short_16","alias_value":"BMX455F6QUTEI4TN","created_at":"2026-07-05T08:05:46.774192+00:00"},{"alias_kind":"pith_short_8","alias_value":"BMX455F6","created_at":"2026-07-05T08:05:46.774192+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY","json":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY.json","graph_json":"https://pith.science/api/pith-number/BMX455F6QUTEI4TNY6PCV4MRVY/graph.json","events_json":"https://pith.science/api/pith-number/BMX455F6QUTEI4TNY6PCV4MRVY/events.json","paper":"https://pith.science/paper/BMX455F6"},"agent_actions":{"view_html":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY","download_json":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY.json","view_paper":"https://pith.science/paper/BMX455F6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.07944&json=true","fetch_graph":"https://pith.science/api/pith-number/BMX455F6QUTEI4TNY6PCV4MRVY/graph.json","fetch_events":"https://pith.science/api/pith-number/BMX455F6QUTEI4TNY6PCV4MRVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY/action/storage_attestation","attest_author":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY/action/author_attestation","sign_citation":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY/action/citation_signature","submit_replication":"https://pith.science/pith/BMX455F6QUTEI4TNY6PCV4MRVY/action/replication_record"}},"created_at":"2026-07-05T08:05:46.774192+00:00","updated_at":"2026-07-05T08:05:46.774192+00:00"}