{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:L6QCPCW2LPTEBYFOL4RDC3JJDR","short_pith_number":"pith:L6QCPCW2","schema_version":"1.0","canonical_sha256":"5fa0278ada5be640e0ae5f22316d291c4ca9a19a4abc789390c62460e31cc55a","source":{"kind":"arxiv","id":"1801.07598","version":1},"attestation_state":"computed","paper":{"title":"Weighted local Weyl laws for elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alejandro Rivera (IF)","submitted_at":"2018-01-22T08:55:25Z","abstract_excerpt":"Let $A$ be an elliptic pseudo-differential operator of order $m$ on a closed manifold $\\mathcal{X}$ of dimension $n>0$, formally positive self-adjoint with respect to some positive smooth density $d\\mu_\\mathcal{X}$. Then, the spectrum of $A$ is made up of a sequence of eigenvalues $(\\lambda_k)_{k\\geq 1}$ whose corresponding eigenfunctions $(e_k)_{k\\geq 1}$ are $C^\\infty$ smooth. Fix $s\\in\\mathbb{R}$ and define \\[ K_L^s(x,y)=\\sum_{0<\\lambda_k\\leq L}\\lambda_k^{-s} e_k(x)\\overline{e_k(y)}\\, .\\] We derive asymptotic formulae near the diagonal for the kernels $K_L^s(x,y)$ when $L\\rightarrow +\\infty"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1801.07598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-22T08:55:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"166fe3c219c0219134f44d643c23322236bb96a82a0365ecac537c5d257ca967","abstract_canon_sha256":"8c4fe280ebdbb0895923d63da53a2a29f2214cb013bf597adc99eeb10ec246b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:12.467439Z","signature_b64":"Q5c5zxeAREE8vwETdnqaU4679yTx8rDfp8ZMTWhHCPEaorU1gF58Jah0RoBVimi7LHNrrzB/e81OSys3YZ42Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fa0278ada5be640e0ae5f22316d291c4ca9a19a4abc789390c62460e31cc55a","last_reissued_at":"2026-05-18T00:25:12.466916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:12.466916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted local Weyl laws for elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alejandro Rivera (IF)","submitted_at":"2018-01-22T08:55:25Z","abstract_excerpt":"Let $A$ be an elliptic pseudo-differential operator of order $m$ on a closed manifold $\\mathcal{X}$ of dimension $n>0$, formally positive self-adjoint with respect to some positive smooth density $d\\mu_\\mathcal{X}$. Then, the spectrum of $A$ is made up of a sequence of eigenvalues $(\\lambda_k)_{k\\geq 1}$ whose corresponding eigenfunctions $(e_k)_{k\\geq 1}$ are $C^\\infty$ smooth. Fix $s\\in\\mathbb{R}$ and define \\[ K_L^s(x,y)=\\sum_{0<\\lambda_k\\leq L}\\lambda_k^{-s} e_k(x)\\overline{e_k(y)}\\, .\\] We derive asymptotic formulae near the diagonal for the kernels $K_L^s(x,y)$ when $L\\rightarrow +\\infty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07598","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1801.07598","created_at":"2026-05-18T00:25:12.466996+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.07598v1","created_at":"2026-05-18T00:25:12.466996+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07598","created_at":"2026-05-18T00:25:12.466996+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6QCPCW2LPTE","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6QCPCW2LPTEBYFO","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6QCPCW2","created_at":"2026-05-18T12:32:33.847187+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR","json":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR.json","graph_json":"https://pith.science/api/pith-number/L6QCPCW2LPTEBYFOL4RDC3JJDR/graph.json","events_json":"https://pith.science/api/pith-number/L6QCPCW2LPTEBYFOL4RDC3JJDR/events.json","paper":"https://pith.science/paper/L6QCPCW2"},"agent_actions":{"view_html":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR","download_json":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR.json","view_paper":"https://pith.science/paper/L6QCPCW2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.07598&json=true","fetch_graph":"https://pith.science/api/pith-number/L6QCPCW2LPTEBYFOL4RDC3JJDR/graph.json","fetch_events":"https://pith.science/api/pith-number/L6QCPCW2LPTEBYFOL4RDC3JJDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR/action/storage_attestation","attest_author":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR/action/author_attestation","sign_citation":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR/action/citation_signature","submit_replication":"https://pith.science/pith/L6QCPCW2LPTEBYFOL4RDC3JJDR/action/replication_record"}},"created_at":"2026-05-18T00:25:12.466996+00:00","updated_at":"2026-05-18T00:25:12.466996+00:00"}