{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PF3AEGN56BAULAWGAC5JJUFSMJ","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":"589565852bc6a6c08c1b7225e63edf1259cd95385cdcd5b3d75a76a366e8f2dd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-06T21:02:00Z","title_canon_sha256":"31cd9c43ea09ccb0a7067cb4c26fb9b981ad1e816f85dd3ad3c516bc943c7056"},"schema_version":"1.0","source":{"id":"1109.1300","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1300","created_at":"2026-05-18T01:16:54Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1300v2","created_at":"2026-05-18T01:16:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1300","created_at":"2026-05-18T01:16:54Z"},{"alias_kind":"pith_short_12","alias_value":"PF3AEGN56BAU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PF3AEGN56BAULAWG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PF3AEGN5","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:2cca30e661a1f07fe60c5b5e05cd27bde55aede51999bc4a80652a439e79570d","target":"graph","created_at":"2026-05-18T01:16:54Z","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":"Consider the Fourier restriction operator associated to a curve in $R^d$, $d\\ge 3$. We prove for various classes of curves the endpoint restricted strong type estimate with respect to affine arclength measure on the curve. An essential ingredient is an interpolation result for multilinear operators with symmetries acting on sequences of vector-valued functions.","authors_text":"Andreas Seeger, Daniel M. Oberlin, Jong-Guk Bak","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-06T21:02:00Z","title":"Restriction of Fourier transforms to curves: An endpoint estimate with affine arclength measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1300","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:d3aa307ebe6a1e96531dacdefa0bb70c44345d7a31df7bffeb57e46b33a9c8cf","target":"record","created_at":"2026-05-18T01:16:54Z","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":"589565852bc6a6c08c1b7225e63edf1259cd95385cdcd5b3d75a76a366e8f2dd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-06T21:02:00Z","title_canon_sha256":"31cd9c43ea09ccb0a7067cb4c26fb9b981ad1e816f85dd3ad3c516bc943c7056"},"schema_version":"1.0","source":{"id":"1109.1300","kind":"arxiv","version":2}},"canonical_sha256":"79760219bdf0414582c600ba94d0b2624bc531a0b24388c2155bca91368b7f11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79760219bdf0414582c600ba94d0b2624bc531a0b24388c2155bca91368b7f11","first_computed_at":"2026-05-18T01:16:54.889123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:54.889123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D6hQKhlTPZGp4AWiI5TYH5r6Rw09tRgnEO6z2qloBZc7kjrdao7R2BJpQIlRv5h5IrVLoPWx9YXrnrV7suasAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:54.889778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1300","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3aa307ebe6a1e96531dacdefa0bb70c44345d7a31df7bffeb57e46b33a9c8cf","sha256:2cca30e661a1f07fe60c5b5e05cd27bde55aede51999bc4a80652a439e79570d"],"state_sha256":"2c75708da4d906c1576ebc00fc2548b10a086804597d846199d70f0a3d518f74"}