{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BYMVD64VLTJEVBX4YGXO4APH4Y","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bc2b852fafa6daeb481833d3ffc4e2958b6915cfdc0d19b4c5d3b5dda0cbdbe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-04T03:29:41Z","title_canon_sha256":"e63b34415ba8303987a0a7315707c090b17af51815c75f4f9b4e970580067e74"},"schema_version":"1.0","source":{"id":"1702.01231","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01231","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01231v2","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01231","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"BYMVD64VLTJE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BYMVD64VLTJEVBX4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BYMVD64V","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:1ee6c890c5047585552ad51c01b2bdf6e78adeb98b270df019c4bee5700ab8e6","target":"graph","created_at":"2026-05-18T00:51:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We provide $L^p \\to L^q$ refinements on some Fourier restriction estimates obtained using polynomial partitioning. Let $S\\subset \\mathbb{R}^3$ be a compact $C^\\infty$ surface with strictly positive second fundamental form. We derive sharp $L^p(S) \\to L^q(\\mathbb{R}^3)$ estimates for the associated Fourier extension operator for $q> 3.25$ and $q\\geq 2p'$ from an estimate of Guth that was used to obtain $L^\\infty(S) \\to L^q(\\mathbb{R}^3)$ bounds for $q>3.25$. We present a slightly weaker result when $S$ is the hyperbolic paraboloid in $\\mathbb{R}^3$ based on the work of Cho and Lee. Finally, we ","authors_text":"Jongchon Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-04T03:29:41Z","title":"Some remarks on Fourier restriction estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01231","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8db670210e774c4f6f3e1e367cf8e5789a2f64807a05da6b7ef445162afdd5e9","target":"record","created_at":"2026-05-18T00:51:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bc2b852fafa6daeb481833d3ffc4e2958b6915cfdc0d19b4c5d3b5dda0cbdbe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-04T03:29:41Z","title_canon_sha256":"e63b34415ba8303987a0a7315707c090b17af51815c75f4f9b4e970580067e74"},"schema_version":"1.0","source":{"id":"1702.01231","kind":"arxiv","version":2}},"canonical_sha256":"0e1951fb955cd24a86fcc1aeee01e7e63a23ef321a9b71fadb2f7056cdf058b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e1951fb955cd24a86fcc1aeee01e7e63a23ef321a9b71fadb2f7056cdf058b5","first_computed_at":"2026-05-18T00:51:02.753866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:02.753866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kk2Nx3Q36SKC1L0F83JeqD6im383Bgi6xALZ5wZBwuNboi+TFyf21WxAKUx/IYV0dC0mPXQSkkBra1Tr3NLrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:02.754600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01231","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8db670210e774c4f6f3e1e367cf8e5789a2f64807a05da6b7ef445162afdd5e9","sha256:1ee6c890c5047585552ad51c01b2bdf6e78adeb98b270df019c4bee5700ab8e6"],"state_sha256":"6e81ef5290e0bc81198eb3ea844690d31041843e29cb346c232adcd3238f53e8"}