{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:2NZUOZEBYJ5OPQEGHJB6QLENGP","short_pith_number":"pith:2NZUOZEB","schema_version":"1.0","canonical_sha256":"d373476481c27ae7c0863a43e82c8d33ee19a66284c4842afd74bfde94ccfd12","source":{"kind":"arxiv","id":"2408.03514","version":4},"attestation_state":"computed","paper":{"title":"A bilinear approach to the finite field restriction problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mark Lewko","submitted_at":"2024-08-07T02:44:06Z","abstract_excerpt":"Let $P$ denote the $3$-dimensional paraboloid over a finite field of odd characteristic in which $-1$ is not a square. We show that the Fourier extension operator associated with $P$ maps $L^2$ to $L^{r}$ for $r > \\frac{32}{9} \\approx 3.555$. In contrast with much of the recent progress on this problem, our argument does not use state-of-the-art incidence estimates but rather proceeds by obtaining estimates on a related bilinear operator. These estimates are based on a geometric result that, roughly speaking, states that a set of points in the finite plane $F^2$ can be decomposed as a union of"},"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":"2408.03514","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-08-07T02:44:06Z","cross_cats_sorted":[],"title_canon_sha256":"252c6097fb21db7faa7c751462489ae198cad9c115cfdff4fe7a2480c833139f","abstract_canon_sha256":"91af1008761e49621e82200151d297a0ec29b35451b1adc0043278f630edde7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:14.906350Z","signature_b64":"u54HV/LV++QwW1ghXTV3majJO5MP5x7BGuj1+htvMtciBn33zUywE+9kjkNDXdMp5hh823017lxpsuVQVN/GAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d373476481c27ae7c0863a43e82c8d33ee19a66284c4842afd74bfde94ccfd12","last_reissued_at":"2026-05-18T02:45:14.905719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:14.905719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A bilinear approach to the finite field restriction problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mark Lewko","submitted_at":"2024-08-07T02:44:06Z","abstract_excerpt":"Let $P$ denote the $3$-dimensional paraboloid over a finite field of odd characteristic in which $-1$ is not a square. We show that the Fourier extension operator associated with $P$ maps $L^2$ to $L^{r}$ for $r > \\frac{32}{9} \\approx 3.555$. In contrast with much of the recent progress on this problem, our argument does not use state-of-the-art incidence estimates but rather proceeds by obtaining estimates on a related bilinear operator. These estimates are based on a geometric result that, roughly speaking, states that a set of points in the finite plane $F^2$ can be decomposed as a union of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.03514","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2408.03514","created_at":"2026-05-18T02:45:14.905817+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.03514v4","created_at":"2026-05-18T02:45:14.905817+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.03514","created_at":"2026-05-18T02:45:14.905817+00:00"},{"alias_kind":"pith_short_12","alias_value":"2NZUOZEBYJ5O","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"2NZUOZEBYJ5OPQEG","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"2NZUOZEB","created_at":"2026-05-18T12:33:37.589309+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/2NZUOZEBYJ5OPQEGHJB6QLENGP","json":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP.json","graph_json":"https://pith.science/api/pith-number/2NZUOZEBYJ5OPQEGHJB6QLENGP/graph.json","events_json":"https://pith.science/api/pith-number/2NZUOZEBYJ5OPQEGHJB6QLENGP/events.json","paper":"https://pith.science/paper/2NZUOZEB"},"agent_actions":{"view_html":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP","download_json":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP.json","view_paper":"https://pith.science/paper/2NZUOZEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.03514&json=true","fetch_graph":"https://pith.science/api/pith-number/2NZUOZEBYJ5OPQEGHJB6QLENGP/graph.json","fetch_events":"https://pith.science/api/pith-number/2NZUOZEBYJ5OPQEGHJB6QLENGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP/action/storage_attestation","attest_author":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP/action/author_attestation","sign_citation":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP/action/citation_signature","submit_replication":"https://pith.science/pith/2NZUOZEBYJ5OPQEGHJB6QLENGP/action/replication_record"}},"created_at":"2026-05-18T02:45:14.905817+00:00","updated_at":"2026-05-18T02:45:14.905817+00:00"}