{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7VLSUDUWSW76Y3CM5MA6Y5BXN2","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":"51580e67827fdc0c58883cb5a8ac469247221d7dc64863a6af81ed8b2d2f8884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-03-02T16:04:26Z","title_canon_sha256":"0057b907326db867828f7c3cf6a80af2dc6198db21ace6b27592da12bc687ab0"},"schema_version":"1.0","source":{"id":"2203.01208","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.01208","created_at":"2026-05-21T01:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"2203.01208v3","created_at":"2026-05-21T01:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.01208","created_at":"2026-05-21T01:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"7VLSUDUWSW76","created_at":"2026-05-21T01:05:01Z"},{"alias_kind":"pith_short_16","alias_value":"7VLSUDUWSW76Y3CM","created_at":"2026-05-21T01:05:01Z"},{"alias_kind":"pith_short_8","alias_value":"7VLSUDUW","created_at":"2026-05-21T01:05:01Z"}],"graph_snapshots":[{"event_id":"sha256:7bf425a48832fbe76e44acd20d50800cc9f9b5e342de84ebbd1d9a36dab1025f","target":"graph","created_at":"2026-05-21T01:05:01Z","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/2203.01208/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We seek to improve the restriction bounds of Neumann data of Laplace eigenfunctions $u_h$ by studying the $L^2$ restriction bounds of Neumann data and their $L^2$ concentration as measured by defect measures. Let $\\gamma$ be a closed smooth curve with unit exterior normal $\\nu$. We can show that $\\| h \\partial_\\nu u_{h} \\|_{L^2(\\Gamma)}=o(1)$ if $\\{u_h\\}$ is tangentially concentrated with respect to $\\gamma$. As a key ingredient of the proof, we give a detailed analysis of the $L^2$ norms over $\\gamma$ of the Neumann data $h\\partial_\\nu u_h$ when mircolocalized away the cotangential direction.","authors_text":"Wu Xianchao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-03-02T16:04:26Z","title":"Improvements in $L^2$ Restriction bounds for Neumann Data along closed curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.01208","kind":"arxiv","version":3},"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:afd56cf87b6dbb5ad474ecbf9b15be025cafdc14674eb0552b1e819082f98d6a","target":"record","created_at":"2026-05-21T01:05:01Z","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":"51580e67827fdc0c58883cb5a8ac469247221d7dc64863a6af81ed8b2d2f8884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-03-02T16:04:26Z","title_canon_sha256":"0057b907326db867828f7c3cf6a80af2dc6198db21ace6b27592da12bc687ab0"},"schema_version":"1.0","source":{"id":"2203.01208","kind":"arxiv","version":3}},"canonical_sha256":"fd572a0e9695bfec6c4ceb01ec74376ea9cf4ecb2148d9a11cfb522c6fd79d76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd572a0e9695bfec6c4ceb01ec74376ea9cf4ecb2148d9a11cfb522c6fd79d76","first_computed_at":"2026-05-21T01:05:01.372408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:01.372408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5GabzJGyH4+jojMUszfPRAwVx7aqsziykoJ1dUj+JYFSXUjW64qqsbGjoDUHieOQBu6J7oJ7BX+8rTewAbDgBg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:01.373140Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.01208","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afd56cf87b6dbb5ad474ecbf9b15be025cafdc14674eb0552b1e819082f98d6a","sha256:7bf425a48832fbe76e44acd20d50800cc9f9b5e342de84ebbd1d9a36dab1025f"],"state_sha256":"8cde3254679699e7303b0b92321a6fe4a46e2e6fcff1c199b0460baab8342ba9"}