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These representations yield strict alternating signs for all forward differences of the sequence $\\bigl(\\mathrm m_{\\mathbb D}(P_n)\\bigr)_{n\\geq1}$, as well as an explicit three-term asymptotic expansion as $n\\to\\infty$."},"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":"2608.01951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-03T09:23:17Z","cross_cats_sorted":[],"title_canon_sha256":"1abea26596dc71a0635422fdebdbc15a06ebf09545c16f76ff2122538c2011a1","abstract_canon_sha256":"675bb9f684207662766cfbabcf100a75a1a98f659548c8f54488ed528955f1fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:10:14.146432Z","signature_b64":"tInmItN0pEOyBUO87wEcIvHQjG4jfFrGi6ysXL/nhERD3heJmSfo12x9UxYyEYzP7ILCywtdQ1Bqk1w8uQ6ZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d89703588cc99d17c5a96db8bc0c981700a091fd7d83b08e669df26f5c63b9b0","last_reissued_at":"2026-08-04T02:10:14.144887Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:10:14.144887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral Representations and Asymptotics for a Family of Areal Mahler Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Quanyu Tang, Shu Zhang","submitted_at":"2026-08-03T09:23:17Z","abstract_excerpt":"We answer a problem posed by Matilde Lal\\'in concerning the areal Mahler measures of the multivariable polynomial family $$\n  P_n(x_1,\\ldots,x_n,u)\n  =\n  \\prod_{j=1}^n(1+x_j)\n  +\n  u\\prod_{j=1}^n(1-x_j),\n  \\qquad n\\geq1. $$ Using a probabilistic reformulation, we derive convolution and one-dimensional Fourier integral representations for $\\mathrm m_{\\mathbb D}(P_n)$. 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