{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6R46R5NUWY7TLNKLE3X5MS4QZJ","short_pith_number":"pith:6R46R5NU","schema_version":"1.0","canonical_sha256":"f479e8f5b4b63f35b54b26efd64b90ca6a12511cbc1967f7883307d6ddf8db1f","source":{"kind":"arxiv","id":"1804.09845","version":11},"attestation_state":"computed","paper":{"title":"$\\ell^p$-improving inequalities for Discrete Spherical Averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael T. Lacey, Robert Kesler","submitted_at":"2018-04-26T01:10:28Z","abstract_excerpt":"Let $ \\lambda ^2 \\in \\mathbb N $, and in dimensions $ d\\geq 5$, let $ A_{\\lambda } f (x)$ denote the average of $ f \\;:\\; \\mathbb Z ^{d} \\to \\mathbb R $ over the lattice points on the sphere of radius $\\lambda$ centered at $x$. We prove $ \\ell ^{p}$ improving properties of $ A_{\\lambda }$. \\begin{equation*} \\lVert A_{\\lambda }\\rVert_{\\ell ^{p} \\to \\ell ^{p'}} \\leq C_{d,p, \\omega (\\lambda ^2 )} \\lambda ^{d ( 1-\\frac{2}p)}, \\qquad \\tfrac{d-1}{d+1} < p \\leq \\frac{d} {d-2}. \\end{equation*} It holds in dimension $ d =4$ for odd $ \\lambda ^2 $. The dependence is in terms of $ \\omega (\\lambda ^2 )$, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.09845","kind":"arxiv","version":11},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-26T01:10:28Z","cross_cats_sorted":[],"title_canon_sha256":"4234900afc16a34bd79f4b40104a3fcb04bcc97f1a19f5cf1bd335fddf1871cd","abstract_canon_sha256":"fde313bd49acea2d51eef0dfa4bff7254bb9b8e28433d813faf2320dd38d1d01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:45:49.252037Z","signature_b64":"Mu0uDMUzBkGIDogHABPJrPBp0jmexXSKnGdO16k3lbNcM3zA/xyorWLtHdghSgEwueI0ANHMNPnSVI1IKO0oCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f479e8f5b4b63f35b54b26efd64b90ca6a12511cbc1967f7883307d6ddf8db1f","last_reissued_at":"2026-07-05T00:45:49.251592Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:45:49.251592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\ell^p$-improving inequalities for Discrete Spherical Averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael T. Lacey, Robert Kesler","submitted_at":"2018-04-26T01:10:28Z","abstract_excerpt":"Let $ \\lambda ^2 \\in \\mathbb N $, and in dimensions $ d\\geq 5$, let $ A_{\\lambda } f (x)$ denote the average of $ f \\;:\\; \\mathbb Z ^{d} \\to \\mathbb R $ over the lattice points on the sphere of radius $\\lambda$ centered at $x$. We prove $ \\ell ^{p}$ improving properties of $ A_{\\lambda }$. \\begin{equation*} \\lVert A_{\\lambda }\\rVert_{\\ell ^{p} \\to \\ell ^{p'}} \\leq C_{d,p, \\omega (\\lambda ^2 )} \\lambda ^{d ( 1-\\frac{2}p)}, \\qquad \\tfrac{d-1}{d+1} < p \\leq \\frac{d} {d-2}. \\end{equation*} It holds in dimension $ d =4$ for odd $ \\lambda ^2 $. The dependence is in terms of $ \\omega (\\lambda ^2 )$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09845","kind":"arxiv","version":11},"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/1804.09845/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":"1804.09845","created_at":"2026-07-05T00:45:49.251649+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.09845v11","created_at":"2026-07-05T00:45:49.251649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09845","created_at":"2026-07-05T00:45:49.251649+00:00"},{"alias_kind":"pith_short_12","alias_value":"6R46R5NUWY7T","created_at":"2026-07-05T00:45:49.251649+00:00"},{"alias_kind":"pith_short_16","alias_value":"6R46R5NUWY7TLNKL","created_at":"2026-07-05T00:45:49.251649+00:00"},{"alias_kind":"pith_short_8","alias_value":"6R46R5NU","created_at":"2026-07-05T00:45:49.251649+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.08893","citing_title":"Sharp $\\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ","json":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ.json","graph_json":"https://pith.science/api/pith-number/6R46R5NUWY7TLNKLE3X5MS4QZJ/graph.json","events_json":"https://pith.science/api/pith-number/6R46R5NUWY7TLNKLE3X5MS4QZJ/events.json","paper":"https://pith.science/paper/6R46R5NU"},"agent_actions":{"view_html":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ","download_json":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ.json","view_paper":"https://pith.science/paper/6R46R5NU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.09845&json=true","fetch_graph":"https://pith.science/api/pith-number/6R46R5NUWY7TLNKLE3X5MS4QZJ/graph.json","fetch_events":"https://pith.science/api/pith-number/6R46R5NUWY7TLNKLE3X5MS4QZJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ/action/storage_attestation","attest_author":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ/action/author_attestation","sign_citation":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ/action/citation_signature","submit_replication":"https://pith.science/pith/6R46R5NUWY7TLNKLE3X5MS4QZJ/action/replication_record"}},"created_at":"2026-07-05T00:45:49.251649+00:00","updated_at":"2026-07-05T00:45:49.251649+00:00"}