{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CP3LNEU6IIH3CF5X66HSTAFZ3I","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":"5ea1da3d45cfd3388ea2e0bf958d7d4a76e1e514193f60807b6dfdba83490d59","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-13T15:20:23Z","title_canon_sha256":"0971c0f80799a2cfe513b5ec2bafae4929fb32631b156d1737d2e0e999d48840"},"schema_version":"1.0","source":{"id":"1010.2683","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2683","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2683v1","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2683","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"CP3LNEU6IIH3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CP3LNEU6IIH3CF5X","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CP3LNEU6","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:8062bb88ad3fae82d61ca21ea88adcae1559eed8a2aaf7cf85ebcf3700f1e175","target":"graph","created_at":"2026-05-18T04:01:23Z","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 eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in $\\R^d$, $d \\geq 2$. In particular, we derive upper bounds on Riesz means of order $\\sigma \\geq 3/2$, that improve the sharp Berezin inequality by a negative second term. This remainder term depends on geometric properties of the boundary of the set and reflects the correct order of growth in the semi-classical limit. Under certain geometric conditions these results imply new lower bounds on individual eigenvalues, which improve the Li-Yau inequality.","authors_text":"Ari Laptev, Leander Geisinger, Timo Weidl","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-13T15:20:23Z","title":"Geometrical Versions of improved Berezin-Li-Yau Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2683","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":"sha256:62ff0adc8a55ae5bfb1db31d80fa2f7a53bdb7a618ce352a3d13b85f95c61086","target":"record","created_at":"2026-05-18T04:01:23Z","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":"5ea1da3d45cfd3388ea2e0bf958d7d4a76e1e514193f60807b6dfdba83490d59","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-13T15:20:23Z","title_canon_sha256":"0971c0f80799a2cfe513b5ec2bafae4929fb32631b156d1737d2e0e999d48840"},"schema_version":"1.0","source":{"id":"1010.2683","kind":"arxiv","version":1}},"canonical_sha256":"13f6b6929e420fb117b7f78f2980b9da039ba2f4d121a9611e85c597d025f3f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13f6b6929e420fb117b7f78f2980b9da039ba2f4d121a9611e85c597d025f3f7","first_computed_at":"2026-05-18T04:01:23.348044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:23.348044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PIFct2PiOZSZwj/4cdZj36QYH6I/nX0vjbTaMK5Jprg+Gmd7+9OMh9D7cBp5LMEzzvKgoP0R8IhkHvKpXvBvDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:23.348552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2683","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62ff0adc8a55ae5bfb1db31d80fa2f7a53bdb7a618ce352a3d13b85f95c61086","sha256:8062bb88ad3fae82d61ca21ea88adcae1559eed8a2aaf7cf85ebcf3700f1e175"],"state_sha256":"63bc32de88dfc43c345c050213b2da49f582f7b499e14a1f372bdc8a98faffae"}