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We prove that, for a broad class of sequences, $\\ddot{H}_n$ admits a remarkably simple product evaluation. This mirrors the behaviour of the classical Hankel determinant $H_n$, but with two key distinctions: the class of sequences for which such formulas are known is far larger in the classical case; and, whereas $H_n$ enjoys a single universa"},"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":"2607.08279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-09T09:22:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"19974c8bc0510a638f8b656dc8d11c9f8a6e2c9ee145544ef1906adfc104aa0f","abstract_canon_sha256":"37859685c042ddb7c85ccbc05be689f23d72658598b3ed983881518b11a75b9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:31.695900Z","signature_b64":"g4lcDY+vbbQ3Ae7iXOgPLS3+oz33o5Gy5prZd5BtQibPADa56u+K1+IU1eOKyfnqZCmiZZf0qmYIa4sb8GZTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38269e46b9211624320d007663119b57a46ccc0299d2d70e24238ccf5aafe91d","last_reissued_at":"2026-07-10T01:19:31.695543Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:31.695543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dilated Hankel determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Guo-Niu Han","submitted_at":"2026-07-09T09:22:18Z","abstract_excerpt":"For a sequence $\\mathbf a=(a_0,a_1,\\dots)$ we define its dilated Hankel determinant $\\ddot{H}_n(\\mathbf a)=\\det(a_{2i+j})_{0\\le i,j\\le n-1}$, the minor of the infinite Hankel matrix $(a_{i+j})$ formed from the even-indexed rows and the first $n$ columns. 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