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We investigate the asymptotic behavior of the operator norms ${{\\bf R}_{\\mathbb{S}^{d-1}}}(p\\to q)$ and ${\\bf R}_{\\mathbb{S}^{d-1}} (p\\to q;\\textrm{rad})$ as the dimension $d$ tends to infinity. We further establish a dimension-free endpoint Stein-Tomas inequality for radial functions, togethe"},"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":"2412.03942","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-12-05T07:45:03Z","cross_cats_sorted":[],"title_canon_sha256":"118f069a55ef5810d11c4339d5f26c756709bd58133152c7d09e12f5c103ff00","abstract_canon_sha256":"9fdef90beb178798a78693553fe24e20702172f00de3ca7d3d1ea19ac12e601c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:37.081263Z","signature_b64":"fInBgU5Q38UXPzBVpskpecwvMzA3KHToIXzPDMGSaY86MutGZ9Oc4anYFQNqq4MMslJUA0ckbu/Nl9R+FzN6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eee936855c41dcc8cc30a727c7d9ae24faa6a5fc55b90b96c13d790d4bd16a0d","last_reissued_at":"2026-07-05T11:05:37.080777Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:37.080777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimension-free Fourier restriction inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Diogo Oliveira e Silva","submitted_at":"2024-12-05T07:45:03Z","abstract_excerpt":"Let ${{\\bf R}_{\\mathbb{S}^{d-1}}}(p\\to q)$ denote the best constant for the $L^p(\\mathbb{R}^d)\\to L^q(\\mathbb{S}^{d-1})$ Fourier restriction inequality to the unit sphere $\\mathbb{S}^{d-1}$, and let ${\\bf R}_{\\mathbb{S}^{d-1}} (p\\to q;\\textrm{rad})$ denote the corresponding constant for radial functions. We investigate the asymptotic behavior of the operator norms ${{\\bf R}_{\\mathbb{S}^{d-1}}}(p\\to q)$ and ${\\bf R}_{\\mathbb{S}^{d-1}} (p\\to q;\\textrm{rad})$ as the dimension $d$ tends to infinity. We further establish a dimension-free endpoint Stein-Tomas inequality for radial functions, togethe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03942","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/2412.03942/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":"2412.03942","created_at":"2026-07-05T11:05:37.080843+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.03942v2","created_at":"2026-07-05T11:05:37.080843+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.03942","created_at":"2026-07-05T11:05:37.080843+00:00"},{"alias_kind":"pith_short_12","alias_value":"53UTNBK4IHOM","created_at":"2026-07-05T11:05:37.080843+00:00"},{"alias_kind":"pith_short_16","alias_value":"53UTNBK4IHOMRTBQ","created_at":"2026-07-05T11:05:37.080843+00:00"},{"alias_kind":"pith_short_8","alias_value":"53UTNBK4","created_at":"2026-07-05T11:05:37.080843+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.01359","citing_title":"Inequalities in Fourier analysis on binary cubes","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET","json":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET.json","graph_json":"https://pith.science/api/pith-number/53UTNBK4IHOMRTBQU4T4PWNOET/graph.json","events_json":"https://pith.science/api/pith-number/53UTNBK4IHOMRTBQU4T4PWNOET/events.json","paper":"https://pith.science/paper/53UTNBK4"},"agent_actions":{"view_html":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET","download_json":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET.json","view_paper":"https://pith.science/paper/53UTNBK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.03942&json=true","fetch_graph":"https://pith.science/api/pith-number/53UTNBK4IHOMRTBQU4T4PWNOET/graph.json","fetch_events":"https://pith.science/api/pith-number/53UTNBK4IHOMRTBQU4T4PWNOET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET/action/storage_attestation","attest_author":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET/action/author_attestation","sign_citation":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET/action/citation_signature","submit_replication":"https://pith.science/pith/53UTNBK4IHOMRTBQU4T4PWNOET/action/replication_record"}},"created_at":"2026-07-05T11:05:37.080843+00:00","updated_at":"2026-07-05T11:05:37.080843+00:00"}