{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B75YQV5ILXHLQWIEFVYMA7VUBG","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":"af0fe34423922c15e0808998296f6291687040176d6b248404476f5058e5f935","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T23:51:18Z","title_canon_sha256":"03965e0fe61de124938c3722298c9d0d63504e089d24e040eb01edcba911badf"},"schema_version":"1.0","source":{"id":"1510.07724","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07724","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07724v3","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07724","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"B75YQV5ILXHL","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B75YQV5ILXHLQWIE","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B75YQV5I","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:173db4664980f7a876529a923a9d2516fc9d384f65d7e6b5f06018e102d9bd70","target":"graph","created_at":"2026-05-18T00:43:39Z","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":"We prove a Kakeya-Nikodym bound on eigenfunctions and quasimodes, which sharpens a result of the authors and extends it to higher dimensions. As in the prior work, the key intermediate step is to prove a microlocal version of these estimates, which involves a phase space decomposition of these modes which is essentially invariant under the bicharacteristic/geodesic flow. In a companion paper, it will be seen that these sharpened estimates yield improved $L^q(M)$ bounds on eigenfunctions in the presence of nonpositive curvature when $2 < q < \\frac{2(d+1)}{d-1}$.","authors_text":"Christopher D. Sogge, Matthew D. Blair","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T23:51:18Z","title":"Refined and Microlocal Kakeya-Nikodym Bounds of Eigenfunctions in Higher Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07724","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:ef6864b0d84eb182c97433baf442e383c858de0c9db8cdace187f0d89e38b7ad","target":"record","created_at":"2026-05-18T00:43:39Z","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":"af0fe34423922c15e0808998296f6291687040176d6b248404476f5058e5f935","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-26T23:51:18Z","title_canon_sha256":"03965e0fe61de124938c3722298c9d0d63504e089d24e040eb01edcba911badf"},"schema_version":"1.0","source":{"id":"1510.07724","kind":"arxiv","version":3}},"canonical_sha256":"0ffb8857a85dceb859042d70c07eb409af46232ed0f4b869b55597e80231e6b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ffb8857a85dceb859042d70c07eb409af46232ed0f4b869b55597e80231e6b8","first_computed_at":"2026-05-18T00:43:39.845935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:39.845935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0lLZ02KcReGrVg4fgQQ9F/qFGXY+h3Akz4zcnFs/+O3jfJyX+/JOPcsO3BDwjxxwMP0qQis59k/rfcEklLoNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:39.846552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07724","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef6864b0d84eb182c97433baf442e383c858de0c9db8cdace187f0d89e38b7ad","sha256:173db4664980f7a876529a923a9d2516fc9d384f65d7e6b5f06018e102d9bd70"],"state_sha256":"449d154aa57ce2f3726d58445a567ba4f56e2ede25c7af27d1d1af8db48c4333"}