{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SPZ7FVJB2GNGF2U5KU3HZYTZ5Q","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":"76d972b967568a96c87865dc7f6902e8477eb258b1e658633c0f3aa019c2b362","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-22T18:10:14Z","title_canon_sha256":"ffefa384747d41bb2f3c6b098877613b770139e2fb875ce66532229b2c4fd24f"},"schema_version":"1.0","source":{"id":"1509.06705","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06705","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06705v3","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06705","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"SPZ7FVJB2GNG","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SPZ7FVJB2GNGF2U5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SPZ7FVJB","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:39b1032c7ba5db00d5c67d3d9e2b9d04e55a4e5859252a412a31a2c27b7389a3","target":"graph","created_at":"2026-05-18T00:47:21Z","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 study the Dirichlet eigenvalues of the Laplacian on a convex domain in $\\mathbb{R}^n$, with $n\\geq 2$. In particular, we generalize and improve upper bounds for the Riesz means of order $\\sigma\\geq 3/2$ established in an article by Geisinger, Laptev and Weidl. This is achieved by refining estimates for a negative second term in the Berezin inequality. The obtained remainder term reflects the correct order of growth in the semi-classical limit and depends only on the measure of the boundary of the domain. We emphasize that such an improvement is for general $\\Omega\\subset\\mathbb{R}^n$ not po","authors_text":"Simon Larson","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-22T18:10:14Z","title":"On the remainder term of the Berezin inequality on a convex domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06705","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":"sha256:30c5e5f975e9457fb22fdad0048ac9a895fbb2017391206e3d72b0e67c574611","target":"record","created_at":"2026-05-18T00:47:21Z","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":"76d972b967568a96c87865dc7f6902e8477eb258b1e658633c0f3aa019c2b362","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-22T18:10:14Z","title_canon_sha256":"ffefa384747d41bb2f3c6b098877613b770139e2fb875ce66532229b2c4fd24f"},"schema_version":"1.0","source":{"id":"1509.06705","kind":"arxiv","version":3}},"canonical_sha256":"93f3f2d521d19a62ea9d55367ce279ec0132dc571035338201533dd54be5d8bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93f3f2d521d19a62ea9d55367ce279ec0132dc571035338201533dd54be5d8bc","first_computed_at":"2026-05-18T00:47:21.256450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:21.256450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"si3eys+u8DYCcUshgL4lfJ8+Iy4Sy/aUEosyKfvA4BkCXJVomDGx5/rj95W6qLpoPZpstDCAqrpTj9fNQ2hmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:21.257059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06705","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30c5e5f975e9457fb22fdad0048ac9a895fbb2017391206e3d72b0e67c574611","sha256:39b1032c7ba5db00d5c67d3d9e2b9d04e55a4e5859252a412a31a2c27b7389a3"],"state_sha256":"6cae4b63b0ddcfc84626f0b9f385fc67a7b51d8fa3d3c6a592467588d9761c2d"}