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Let $A$ be a polyhomogeneous elliptic pseudo-differential operator of positive order $m$ on $\\mathcal{M}$ which is symmetric for the $L^2$ scalar product defined by $d\\mu_{\\mathcal{M}}$. For each $L>0$, the space $U_L=\\bigoplus_{\\lambda\\leq L}Ker(A-\\lambda Id)$ is a finite dimensional subspace of $C^\\infty(\\mathcal{M})$. Let $\\Pi_L$ be the spectral projector onto $U_L$. Given $s\\in\\mathbb{R}$, we compute the asymptotics of the integral kernel $K_L$ of $\\Pi_LA^{-s}$ in the cases"},"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":"1611.02018","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-07T12:28:19Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"256a602845e39882874e8d23e27246fccb2448d0b026c86ea6a2efd4f1c82d71","abstract_canon_sha256":"7deb1ba3eaee1a99c4a4b8f8eb2b2c9a6f065540d2ae618f7be4982a0c656b31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:50.822415Z","signature_b64":"JwjAKMh7+wEX7SjX0Q1fl3LpuSutTjDcCJpmQfXlyWM4T/2/M+7hLVBfMqakVXfRNdkzg22RTOokHDwHog++AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f445194032cee5b70630e5574aea27d61a79b569f0062c339178a31ea977881b","last_reissued_at":"2026-05-18T00:12:50.821673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:50.821673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anomalies in local Weyl laws and applications to random topology at critical dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.SP","authors_text":"Alejandro Rivera","submitted_at":"2016-11-07T12:28:19Z","abstract_excerpt":"Let $\\mathcal{M}$ be a smooth manifold of positive dimension $n$ equipped with a smooth density $d\\mu_{\\mathcal{M}}$. 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