{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RPIBNSN6UA6REDCXAH5EW2X3RG","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":"2d95f4f965fbd8a2289ba86912b6a8193c97c1f17f7616ccbb7c069fbbc0b10d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-28T03:16:26Z","title_canon_sha256":"7883aa7074df26712eaed77a0e9ea1d6a602e5d597c33d62b06650335e989701"},"schema_version":"1.0","source":{"id":"1607.08302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08302","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08302v1","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08302","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"RPIBNSN6UA6R","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RPIBNSN6UA6REDCX","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RPIBNSN6","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:8df368a030c56f50b9a117ad80767d5f912e25f9d6c1f62b077c0e89830996e2","target":"graph","created_at":"2026-05-18T01:10:19Z","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":"For any $\\alpha\\in(0,d)$, we construct Cantor sets in $\\mathbb{R}^d$ of Hausdorff dimension $\\alpha$ such that the associated natural measure $\\mu$ obeys the restriction estimate $\\| \\widehat{f d\\mu} \\|_{p} \\leq C_p \\| f \\|_{L^2(\\mu)}$ for all $p>2d/\\alpha$. This range is optimal except for the endpoint. This extends the earlier work of Chen-Seeger and Shmerkin-Suomala, where a similar result was obtained by different methods for $\\alpha=d/k$ with $k\\in\\mathbb{N}$. Our proof is based on the decoupling techniques of Bourgain-Demeter and a theorem of Bourgain on the existence of $\\Lambda(p)$ set","authors_text":"Hong Wang, Izabella Laba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-28T03:16:26Z","title":"Decoupling and near-optimal restriction estimates for Cantor sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08302","kind":"arxiv","version":1},"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:e5ad8778a8f71555073813e03bc64bba13bea81142af3193a8befefa91328c07","target":"record","created_at":"2026-05-18T01:10:19Z","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":"2d95f4f965fbd8a2289ba86912b6a8193c97c1f17f7616ccbb7c069fbbc0b10d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-28T03:16:26Z","title_canon_sha256":"7883aa7074df26712eaed77a0e9ea1d6a602e5d597c33d62b06650335e989701"},"schema_version":"1.0","source":{"id":"1607.08302","kind":"arxiv","version":1}},"canonical_sha256":"8bd016c9bea03d120c5701fa4b6afb8996f05ad16673553b57e08389be72b454","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bd016c9bea03d120c5701fa4b6afb8996f05ad16673553b57e08389be72b454","first_computed_at":"2026-05-18T01:10:19.442025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:19.442025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KxJzDUXc+G/Nx1Z3D7IsXmoMMS6UuCZMXweJUyaF/C7OKvIwCQaGHeh0PGg24ENa97/wXpbSzdeKQfjCzJ9cBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:19.442585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5ad8778a8f71555073813e03bc64bba13bea81142af3193a8befefa91328c07","sha256:8df368a030c56f50b9a117ad80767d5f912e25f9d6c1f62b077c0e89830996e2"],"state_sha256":"7f938baedd6c262c663e10694e2e84be119f5ea22ef49925806bd0a35458395e"}