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For any $a \\in \\Gamma(\\text{End}(V))$, we consider the asymptotics $\\text{Tr} (a e^{-tP}) \\underset{t \\downarrow 0^+}{\\sim} \\,\\sum_{r=0}^\\infty a_r(a, P)\\,t^{(r-d)/2}$ where the coefficients $a_r(a, P)$ can be written locally as $a_r(a, P)(x) = \\text{tr}[a(x) \\math"},"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":"1707.09657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-30T19:13:51Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.OA"],"title_canon_sha256":"c3ecb018d417070abbf409ed20282c7662ca64748d8a9fa796c00cbc73cf65f7","abstract_canon_sha256":"cf6b52281987b1568f67675a05101f8014f0dd38405191ed7f659b37f7032422"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:58.809815Z","signature_b64":"5da5Xzvgtegh1FUrj2sbnIn/H4+2BFiuDqH7kB+VO+xB/Y3Q2q23UEWI2NBblerCiNwZteAuN0L4mJSvQlD3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bac67c891613d65a3fab37be5ace4a2432186242bedb885640dfe88502f4333","last_reissued_at":"2026-05-17T23:56:58.809171Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:58.809171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.OA"],"primary_cat":"math.DG","authors_text":"Bruno Iochum, Thierry Masson","submitted_at":"2017-07-30T19:13:51Z","abstract_excerpt":"Let $P$ be a Laplace type operator acting on a smooth hermitean vector bundle $V$ of fiber $\\mathbb{C}^N$ over a compact Riemannian manifold given locally by $P= - [g^{\\mu\\nu} u(x)\\partial_\\mu\\partial_\\nu + v^\\nu(x)\\partial_\\nu + w(x)]$ where $u,\\,v^\\nu,\\,w$ are $M_N(\\mathbb{C})$-valued functions with $u(x)$ positive and invertible. 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