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As by-product of a complete solution of all non-planar correlation functions of the renormalised $\\Phi^3$-matrical QFT model, we explicitly construct a Laplacian $\\Delta_t$ on the space of formal parameters $t_i$ satisfying $\\exp(\\sum_{g\\geq 2} N^{2-2g}F_g(t))=\\exp((-\\Delta_t+F_2(t))/N^2)1$ for any $N>0$. The result is achieved via Dyson-Schwinger equations from noncommutative quantum field theory combined with residue techniques from topological recurs"},"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":"1903.12526","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-29T14:04:08Z","cross_cats_sorted":["math.AG","math.MP"],"title_canon_sha256":"4a8e47116c5f6fd304d69f964d36c0467d8d5c2c0506657e4796b25e50c97235","abstract_canon_sha256":"cf1d6e04de45467b6f1c4bedc1ab587ee5732e18870ef3801df456eee3ebbbe1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:03:04.830011Z","signature_b64":"gg5pxkRvkD1hkPWDxPEMH5kQZOWbMuij4n34Y/tjgac1eC7MvZfwC3S/qdxJCFZhQSlQwgCOi/bIZkVVYzs5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07d5650ada59bb2cf5b8186ed9d784f5dd9ba38d335a20f42b61c6cb8ace9695","last_reissued_at":"2026-07-05T06:03:04.829546Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:03:04.829546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Laplacian to compute intersection numbers on $\\bar{\\mathcal{M}}_{g,n}$ and correlation functions in NCQFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Hock, Harald Grosse (Vienna), Raimar Wulkenhaar (M\\\"unster)","submitted_at":"2019-03-29T14:04:08Z","abstract_excerpt":"Let $F_g(t)$ be the generating function of intersection numbers on the moduli spaces $\\bar{\\mathcal{M}}_{g,n}$ of complex curves of genus $g$. As by-product of a complete solution of all non-planar correlation functions of the renormalised $\\Phi^3$-matrical QFT model, we explicitly construct a Laplacian $\\Delta_t$ on the space of formal parameters $t_i$ satisfying $\\exp(\\sum_{g\\geq 2} N^{2-2g}F_g(t))=\\exp((-\\Delta_t+F_2(t))/N^2)1$ for any $N>0$. 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