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We demonstrate using general arguments and explicit examples that whenever the correlation length is finite, local observables converge exponentially fast in the cluster size, $L_{c}$, within Cellular Dynamical Mean Field Theory (CDMFT). This is a faster rate of convergence than the $1/L_{c}^{2}$ behavior of the Dynamical Cluster approximation (DCA) thus refuting the central assertion of their comment."},"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":"cond-mat/0404537","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.str-el","submitted_at":"2004-04-22T18:50:06Z","cross_cats_sorted":[],"title_canon_sha256":"6b9f390e5f3b09c37f1d895bcbcb8515a51e4f675d2f434e4ff68ac62b93e6e3","abstract_canon_sha256":"d56d2a6dc67f6826ef0ca3b543d7684ae4a9479f0f8fc5b5c24728d526433826"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:32.338973Z","signature_b64":"Y6uwQMXrggXThyVac0/eJ7dvBMZrjICg0QPc3hteiSfiuXgq1JzYnNwhyuPy/y+4Hs6V69x0iqMfIZLEi/FkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b36ea6be9653c24931ecd3fd442591fa9cceb61f231813f5364da1b2016332a5","last_reissued_at":"2026-05-18T03:24:32.338031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:32.338031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential Convergence of Cellular Dynamical Mean Field Theory: Reply to the comment by K. 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