{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OBHUTNAACNRKP7ZQWWUUEOXNPA","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":"80de2e422923fbc2e88b3ea3b09cd39df7af5c489951c9409da52eada41e5cc5","cross_cats_sorted":["math.NA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T04:17:38Z","title_canon_sha256":"30b3c30a4736ed359110423d01f251fcad4d4f389e7e39ce898f4a3a101b28b4"},"schema_version":"1.0","source":{"id":"1512.04165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04165","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04165v2","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04165","created_at":"2026-05-18T00:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"OBHUTNAACNRK","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OBHUTNAACNRKP7ZQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OBHUTNAA","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:939039adaff788b65f084f4c8321b1c64357f4521dc743434668ea70d115266a","target":"graph","created_at":"2026-05-18T00:00:46Z","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 smooth bounded domains in $\\mathbb{R}$, we prove upper and lower $L^2$ bounds on the boundary data of Neumann eigenfunctions, and prove quasi-orthogonality of this boundary data in a spectral window. The bounds are tight in the sense that both are independent of eigenvalue; this is achieved by working with an appropriate norm for boundary functions, which includes a `spectral weight', that is, a function of the boundary Laplacian. This spectral weight is chosen to cancel concentration at the boundary that can happen for `whispering gallery' type eigenfunctions. These bounds are closely rel","authors_text":"Alex Barnett, Andrew Hassell, Melissa Tacy","cross_cats":["math.NA","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T04:17:38Z","title":"Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04165","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:ac5f0bc521996631c0fe16430c684241b076782c5055ef3e46c389067400f871","target":"record","created_at":"2026-05-18T00:00:46Z","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":"80de2e422923fbc2e88b3ea3b09cd39df7af5c489951c9409da52eada41e5cc5","cross_cats_sorted":["math.NA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T04:17:38Z","title_canon_sha256":"30b3c30a4736ed359110423d01f251fcad4d4f389e7e39ce898f4a3a101b28b4"},"schema_version":"1.0","source":{"id":"1512.04165","kind":"arxiv","version":2}},"canonical_sha256":"704f49b4001362a7ff30b5a9423aed782442a3f2dd886c1b99ff9928a1b6e4c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"704f49b4001362a7ff30b5a9423aed782442a3f2dd886c1b99ff9928a1b6e4c4","first_computed_at":"2026-05-18T00:00:46.049082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:46.049082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rig91V60U9ipHs4t0xOGyj/pMCgqq06ALuCGtQSD8eLnnm2T0WzmlEAwYd7fntkiHZbmMsatm+6xvWhQvrooAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:46.049474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac5f0bc521996631c0fe16430c684241b076782c5055ef3e46c389067400f871","sha256:939039adaff788b65f084f4c8321b1c64357f4521dc743434668ea70d115266a"],"state_sha256":"16307116f1949adf7655e91ae8519141a94eca415f842d35e6702689777f859d"}