{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:4UGGRY63LYJUNVVVEHJNQKPWFH","short_pith_number":"pith:4UGGRY63","schema_version":"1.0","canonical_sha256":"e50c68e3db5e1346d6b521d2d829f629da4d18368b533bb14ff13bec6e620e7c","source":{"kind":"arxiv","id":"2407.05344","version":1},"attestation_state":"computed","paper":{"title":"The Duffin-Schaeffer conjecture with a moving target","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Felipe A. Ramirez, Manuel Hauke","submitted_at":"2024-07-07T12:35:02Z","abstract_excerpt":"We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension $m \\geq 3$. That is, given $\\mathbf{y}\\in \\mathbb{R}^m$ and $\\psi:\\mathbb{N}\\to\\mathbb{R}_{\\geq 0}$ such that $\\sum (\\varphi(q)\\psi(q)/q)^m = \\infty$, we show that for almost every $\\mathbf{x} \\in\\mathbb{R}^m$ there are infinitely many rational vectors $\\mathbf{a}/q$ such that $\\vert q\\mathbf{x} - \\mathbf{a} - \\mathbf{y}\\vert<\\psi(q)$ and such that each component of $\\mathbf{a}$ is coprime to $q$. This is an inhomogeneous extension of a homogeneous conjecture of Sprind\\v{z}uk which was itself proved in 19"},"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":"2407.05344","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2024-07-07T12:35:02Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"19f60fb557a82fa75d103d122c968c68639b5abdebba379265c1c19c21c98241","abstract_canon_sha256":"b6f88c2c888a62b702a7a0fb34732b41792e9f1a38ae994512011844ed7b23f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:41:11.736614Z","signature_b64":"qvnJbYeWpCnuBAnKgCqbY/88ubrGPRjsuY9UYlxcWXkPFPIeqi77mJksde7Crhi+ulKL98Wts1bY8d6UW5QSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e50c68e3db5e1346d6b521d2d829f629da4d18368b533bb14ff13bec6e620e7c","last_reissued_at":"2026-07-05T08:41:11.736161Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:41:11.736161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Duffin-Schaeffer conjecture with a moving target","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Felipe A. Ramirez, Manuel Hauke","submitted_at":"2024-07-07T12:35:02Z","abstract_excerpt":"We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension $m \\geq 3$. That is, given $\\mathbf{y}\\in \\mathbb{R}^m$ and $\\psi:\\mathbb{N}\\to\\mathbb{R}_{\\geq 0}$ such that $\\sum (\\varphi(q)\\psi(q)/q)^m = \\infty$, we show that for almost every $\\mathbf{x} \\in\\mathbb{R}^m$ there are infinitely many rational vectors $\\mathbf{a}/q$ such that $\\vert q\\mathbf{x} - \\mathbf{a} - \\mathbf{y}\\vert<\\psi(q)$ and such that each component of $\\mathbf{a}$ is coprime to $q$. This is an inhomogeneous extension of a homogeneous conjecture of Sprind\\v{z}uk which was itself proved in 19"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05344","kind":"arxiv","version":1},"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/2407.05344/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":"2407.05344","created_at":"2026-07-05T08:41:11.736223+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.05344v1","created_at":"2026-07-05T08:41:11.736223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.05344","created_at":"2026-07-05T08:41:11.736223+00:00"},{"alias_kind":"pith_short_12","alias_value":"4UGGRY63LYJU","created_at":"2026-07-05T08:41:11.736223+00:00"},{"alias_kind":"pith_short_16","alias_value":"4UGGRY63LYJUNVVV","created_at":"2026-07-05T08:41:11.736223+00:00"},{"alias_kind":"pith_short_8","alias_value":"4UGGRY63","created_at":"2026-07-05T08:41:11.736223+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.13868","citing_title":"Fourier Dimension in Inhomogeneous Duffin--Schaeffer Conjecture","ref_index":26,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH","json":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH.json","graph_json":"https://pith.science/api/pith-number/4UGGRY63LYJUNVVVEHJNQKPWFH/graph.json","events_json":"https://pith.science/api/pith-number/4UGGRY63LYJUNVVVEHJNQKPWFH/events.json","paper":"https://pith.science/paper/4UGGRY63"},"agent_actions":{"view_html":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH","download_json":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH.json","view_paper":"https://pith.science/paper/4UGGRY63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.05344&json=true","fetch_graph":"https://pith.science/api/pith-number/4UGGRY63LYJUNVVVEHJNQKPWFH/graph.json","fetch_events":"https://pith.science/api/pith-number/4UGGRY63LYJUNVVVEHJNQKPWFH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH/action/storage_attestation","attest_author":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH/action/author_attestation","sign_citation":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH/action/citation_signature","submit_replication":"https://pith.science/pith/4UGGRY63LYJUNVVVEHJNQKPWFH/action/replication_record"}},"created_at":"2026-07-05T08:41:11.736223+00:00","updated_at":"2026-07-05T08:41:11.736223+00:00"}