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Hien introduced rapid decay homology group $\\Homo^{rd}_{*}(U, (\\nabla, E))$ associated to an irregular connection $(\\nabla, E)$ on a smooth complex affine variety $U$, and showed that it is the dual group of the algebraic de Rham cohomology group $\\Homo^*_{dR}(U,(\\nabla^{\\vee}, E^{\\vee}))$. On the other hand, F. Pham has already introduced his version of rapid decay homology when $(\\nabla, E)$ is the so-called elementary irregular connection (\\cite{Sab}) in \\cite{Pham}. In this report, we will state a comparison theorem of these homology groups and give an outline of its pro"},"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":"1705.06052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-17T08:53:42Z","cross_cats_sorted":["math.AG","math.AP","math.CV"],"title_canon_sha256":"409615065e5a8fb55ab0658ba0ce5bf0cc51abdd424196867c7d95745dc71e63","abstract_canon_sha256":"c4c5fbd6a3ab6c87241ee0e0a7229189722330dd174d9212d6568a1f1e5b2676"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:19.111141Z","signature_b64":"pqmfwSXaEZZCbMa1ZhnbGJDWqtqIRe/QMTOgy1c5cL/8UC4GcU9HWKSUsrvt9V8fYX6Nvr4EpFQHIOpGMn7qAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"229e91147c112bc17fe8aaf5bde5b62af093d3ced22f6c69c0aff1c260316dea","last_reissued_at":"2026-05-18T00:44:19.110700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:19.110700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the rapid decay homology of F.Pham","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AP","math.CV"],"primary_cat":"math.CA","authors_text":"Saiei-Jaeyeong Matsubara-Heo","submitted_at":"2017-05-17T08:53:42Z","abstract_excerpt":"In \\cite{hien}, M. 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