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We consider the one-particle density matrix $\\gamma(x, y)$ and one-particle kinetic energy density $\\varkappa(x, y)$, $x, y\\in {\\mathbb R}^3$, associated with the eigenfunction $\\psi$. Both functions play a central role in quantum chemistry computations of atomic and molecular bound states: the knowledge of the eigenvalue behaviour of the integral operators ${\\sf{\\Gamma}}$ and ${\\sf{K}}$ with kernels $\\gamma(x, y)$ and $\\varkappa(x, y)$ serves to estimate the error"},"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":"2608.09570","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-08-10T13:07:18Z","cross_cats_sorted":["math.FA","math.MP","math.SP"],"title_canon_sha256":"6d2b1faaa10ddc940f05c77dc50345fa5a78bc8ea3209c98539feb9988b2fe57","abstract_canon_sha256":"36a5d96c456b2b7639044f9ad3945f2e533c0cc8aa44f104ec959a859712e69e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T02:24:31.356486Z","signature_b64":"bGr1ZnOT9dmTiYk2xyMSQaLLaPxF/UORwQUwmAIFQljr36T1CsQVcP1rR4pJtqDP2VAN0erztNR1bH5MsxTFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6aa9c87e8deb3bc9168f2be7db1902961453d22540493d7ef81394b31c0578a","last_reissued_at":"2026-08-11T02:24:31.354831Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T02:24:31.354831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalue asymptotics for the one-particle density matrix and one-particle kinetic energy density operator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Alexander V. 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