{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JMH6MV4TXRDZZ7NBP3FJ6VCBFO","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":"31d8da5787e47b3bc821b5bec74f8d46f4c802c2bb98ef8165d6a78645e6f974","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2021-05-04T17:13:51Z","title_canon_sha256":"f30b8e6684d5ef934882fc4dd57d101a860bfca90e23768182ebfda70640cbae"},"schema_version":"1.0","source":{"id":"2105.01628","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.01628","created_at":"2026-07-05T04:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"2105.01628v4","created_at":"2026-07-05T04:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.01628","created_at":"2026-07-05T04:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"JMH6MV4TXRDZ","created_at":"2026-07-05T04:10:22Z"},{"alias_kind":"pith_short_16","alias_value":"JMH6MV4TXRDZZ7NB","created_at":"2026-07-05T04:10:22Z"},{"alias_kind":"pith_short_8","alias_value":"JMH6MV4T","created_at":"2026-07-05T04:10:22Z"}],"graph_snapshots":[{"event_id":"sha256:28978709f7abc07897d08219af1228a5f082a158d8db131a3de9a4ff9e175f3b","target":"graph","created_at":"2026-07-05T04:10:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.01628/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove sharp smoothing properties of the averaging operator defined by convolution with a measure on a smooth nondegenerate curve $\\gamma$ in $\\mathbb R^d$, $d\\ge 3$. Despite the simple geometric structure of such curves, the sharp smoothing estimates have remained largely unknown except for those in low dimensions. Devising a novel inductive strategy, we obtain the optimal $L^p$ Sobolev regularity estimates, which settle the conjecture raised by Beltran-Guo-Hickman-Seeger. Besides, we show the sharp local smoothing estimates for every $d$. As a result, we establish, for the first time, nont","authors_text":"Hyerim Ko, Sanghyuk Lee, Sewook Oh","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2021-05-04T17:13:51Z","title":"Sharp smoothing properties of averages over curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.01628","kind":"arxiv","version":4},"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:bfdf6fd410a60d52da912310f1289fda47b2e6a919e1f257485af2f60993d8fd","target":"record","created_at":"2026-07-05T04:10:22Z","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":"31d8da5787e47b3bc821b5bec74f8d46f4c802c2bb98ef8165d6a78645e6f974","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2021-05-04T17:13:51Z","title_canon_sha256":"f30b8e6684d5ef934882fc4dd57d101a860bfca90e23768182ebfda70640cbae"},"schema_version":"1.0","source":{"id":"2105.01628","kind":"arxiv","version":4}},"canonical_sha256":"4b0fe65793bc479cfda17eca9f54412b91d7f67ce1021fa305af7bb8b010bbfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0fe65793bc479cfda17eca9f54412b91d7f67ce1021fa305af7bb8b010bbfc","first_computed_at":"2026-07-05T04:10:22.289343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:10:22.289343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tOPIp2DWDvCWlGoKvTsHb22PnkYEJiZ5lGW64pVV5XLaTd1DBzZ7uvK+Jy/kzu/UNRLUMBFckV5THXcmeqbmDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:10:22.289791Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.01628","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfdf6fd410a60d52da912310f1289fda47b2e6a919e1f257485af2f60993d8fd","sha256:28978709f7abc07897d08219af1228a5f082a158d8db131a3de9a4ff9e175f3b"],"state_sha256":"0f7be9824a9397831601872226d265bfa07e3ef2b38ec8a8abcc1858b8c3e618"}