{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Z2UHYUMI4HMTOJ6SZUKVECGLJB","short_pith_number":"pith:Z2UHYUMI","schema_version":"1.0","canonical_sha256":"cea87c5188e1d93727d2cd155208cb487cbaa4478748f6982af7bc40c01aedd6","source":{"kind":"arxiv","id":"2502.09807","version":1},"attestation_state":"computed","paper":{"title":"A note on limsup sets of annuli","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.NT","authors_text":"Benjamin Ward, Mumtaz Hussain","submitted_at":"2025-02-13T22:52:20Z","abstract_excerpt":"We consider the set of points in infinitely many max-norm annuli centred at rational points in $\\mathbb R^{n}$. We give Jarn\\'ik-Besicovitch type theorems for this set in terms of Hausdorff dimension. Interestingly, we find that if the outer radii are decreasing sufficiently slowly, dependent only on the dimension $n$, and the thickness of the annuli is decreasing rapidly then the dimension of the set tends towards $n-1$. We also consider various other forms of annuli including rectangular annuli and quasi-annuli described by the difference between balls of two different norms. Our results are"},"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":"2502.09807","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-13T22:52:20Z","cross_cats_sorted":["math.DS","math.MG"],"title_canon_sha256":"c6a9a08228c494b180e892429999467a5083a5ba2ccfd9d28e824b6f3270b028","abstract_canon_sha256":"7b6e827f77e983f99eaff3a166847a3d799b52800f8d27c8061a9a8313e0841f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:12.415894Z","signature_b64":"7JJh4XzI2F1wooOtK/vTpTEgHdbDRB8m6Z0IM78lTFjMnlWsAxExRs9Bk8xMS4h75kVfasLO+nYKBi6UanWkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea87c5188e1d93727d2cd155208cb487cbaa4478748f6982af7bc40c01aedd6","last_reissued_at":"2026-07-05T10:14:12.415444Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:12.415444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on limsup sets of annuli","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.NT","authors_text":"Benjamin Ward, Mumtaz Hussain","submitted_at":"2025-02-13T22:52:20Z","abstract_excerpt":"We consider the set of points in infinitely many max-norm annuli centred at rational points in $\\mathbb R^{n}$. We give Jarn\\'ik-Besicovitch type theorems for this set in terms of Hausdorff dimension. Interestingly, we find that if the outer radii are decreasing sufficiently slowly, dependent only on the dimension $n$, and the thickness of the annuli is decreasing rapidly then the dimension of the set tends towards $n-1$. We also consider various other forms of annuli including rectangular annuli and quasi-annuli described by the difference between balls of two different norms. Our results are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09807","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/2502.09807/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":"2502.09807","created_at":"2026-07-05T10:14:12.415503+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.09807v1","created_at":"2026-07-05T10:14:12.415503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09807","created_at":"2026-07-05T10:14:12.415503+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2UHYUMI4HMT","created_at":"2026-07-05T10:14:12.415503+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2UHYUMI4HMTOJ6S","created_at":"2026-07-05T10:14:12.415503+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2UHYUMI","created_at":"2026-07-05T10:14:12.415503+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/Z2UHYUMI4HMTOJ6SZUKVECGLJB","json":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB.json","graph_json":"https://pith.science/api/pith-number/Z2UHYUMI4HMTOJ6SZUKVECGLJB/graph.json","events_json":"https://pith.science/api/pith-number/Z2UHYUMI4HMTOJ6SZUKVECGLJB/events.json","paper":"https://pith.science/paper/Z2UHYUMI"},"agent_actions":{"view_html":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB","download_json":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB.json","view_paper":"https://pith.science/paper/Z2UHYUMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.09807&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2UHYUMI4HMTOJ6SZUKVECGLJB/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2UHYUMI4HMTOJ6SZUKVECGLJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB/action/storage_attestation","attest_author":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB/action/author_attestation","sign_citation":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB/action/citation_signature","submit_replication":"https://pith.science/pith/Z2UHYUMI4HMTOJ6SZUKVECGLJB/action/replication_record"}},"created_at":"2026-07-05T10:14:12.415503+00:00","updated_at":"2026-07-05T10:14:12.415503+00:00"}