{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TKWIA6V3QQP3P6TIHAJ32WKFGV","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":"f896f8d2907b460775ad40baf399d8046036746713b8d1034847c7056f697bce","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-12T00:19:46Z","title_canon_sha256":"83f09fafef01c47a9a17c005ffd43d903f957a2406dadf10e6297d10af5519b9"},"schema_version":"1.0","source":{"id":"1307.3298","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3298","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3298v2","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3298","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"TKWIA6V3QQP3","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TKWIA6V3QQP3P6TI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TKWIA6V3","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:ed9a3f24864ede03a7817db2afd02754d45e2f61da056b7f2e8e4df59e6c0fb1","target":"graph","created_at":"2026-05-18T02:41:42Z","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":"In this note we consider the adjoint restriction estimate for hypersurface under additional regularity assumption. We obtain the optimal $H^s$-$L^q$ estimate and its mixed norm generalization. As applications we prove some weighted Strichartz estimates for the propagator $e^{it(-\\Delta)^{\\alpha/2}}\\varphi$, $\\alpha>0$.","authors_text":"Sanghyuk Lee, Yonggeun Cho, Zihua Guo","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-12T00:19:46Z","title":"A Sobolev estimate for the adjoint restriction operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3298","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:aff39ae372b350c742cddbc8c4fa5d84bc9b5ef2d2ee48539def1f0b91407501","target":"record","created_at":"2026-05-18T02:41:42Z","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":"f896f8d2907b460775ad40baf399d8046036746713b8d1034847c7056f697bce","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-12T00:19:46Z","title_canon_sha256":"83f09fafef01c47a9a17c005ffd43d903f957a2406dadf10e6297d10af5519b9"},"schema_version":"1.0","source":{"id":"1307.3298","kind":"arxiv","version":2}},"canonical_sha256":"9aac807abb841fb7fa683813bd59453558b176a72ff4999c98b3b98e05a008c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9aac807abb841fb7fa683813bd59453558b176a72ff4999c98b3b98e05a008c7","first_computed_at":"2026-05-18T02:41:42.324980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:42.324980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o3rYX26uTSyWfIIJuj4PROsQTtKPeKGJC9k0yFoDUD3TVKUyRsrZ5rze+uNMUJKJbcXPSwfAGiFAezzESKOzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:42.325666Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3298","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aff39ae372b350c742cddbc8c4fa5d84bc9b5ef2d2ee48539def1f0b91407501","sha256:ed9a3f24864ede03a7817db2afd02754d45e2f61da056b7f2e8e4df59e6c0fb1"],"state_sha256":"dd8378d52cbb2f9894c908390159d7f89f447b0c45762e3e33cbc60b4df678d5"}