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Here $\\lambda\\in (0,1)$ is the contraction ratio and ${\\mathcal O}$ is an orthogonal matrix. Given a positive probability vector $p$, there is a unique invariant (stationary) measure for the IFS, called (in this case) a homogeneous self-similar measure, which we denote $\\mu(\\lambda {\\mathcal O}, {\\mathcal D}, p)$, where ${\\mathcal D} = \\{a_0,\\ldots,a_m\\}$ is the set of ``vector digits''. We obtain two results on Fourier decay fo"},"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":"2508.14698","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-20T13:23:13Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3263a2927fa0e198f04cc8f2bc9dc18c73f83de71d07caac88cda90541a18168","abstract_canon_sha256":"6ddd0f1c219edcc7fe91cb1ff6400da51222abe1612255c8489ff3964506be7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:36.970565Z","signature_b64":"TStTJm0uRboQGUauRvRFMucE/HxaQyXmK9Rxr8MorOd39P30LMS4VyzoiQ24Wl0KuxRTDDG0f9mfn3SvLzouDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"695677231b01bba3dd412b80d91a56d607ff93c49c9531ab1d8344092fd6e112","last_reissued_at":"2026-07-05T11:56:36.970157Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:36.970157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourier decay and absolute continuity for typical homogeneous self-similar measures in ${\\mathbb R}^d$ for $d\\ge 3$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Boris Solomyak","submitted_at":"2025-08-20T13:23:13Z","abstract_excerpt":"We consider iterated function systems (IFS) in ${\\mathbb R}^d$ for $d\\ge 3$ of the form $\\{f_j(x) = \\lambda {\\mathcal O} x + a_j\\}_{j=0}^m$, with $a_0=0$ and $m\\ge 1$. 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