Addendum to: Periods and factors of weak model sets

Gerhard Keller, Christoph Richard, Nicolae Strungaru

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s addendum proves Theorems B1’ and B2’ using Moody-type uniform distribution (Proposition 2.1), an a.e. injectivity argument (Lemmas 3.1–3.2), and then passing to the quotient by the Haar-period group to handle general windows; the candidate solution follows precisely this scheme. Minor issues in the candidate include averaging along Γ instead of G and an unnecessary (and slightly inaccurate) remark about π_G|_L implying a zero G-component difference; neither affects the core argument or the conclusions.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The addendum cleanly extends prior results on torus parametrisations and Mirsky measures from compact (up to null) windows to arbitrary measurable, relatively compact windows, with concise proofs leveraging Moody’s uniform distribution and amenable ergodic theorems. Correctness appears solid, and the implications for spectral/diffraction analysis are clearly signposted. Minor clarifications would further aid readability (e.g., explicit statements about where positivity of m\_H(W) is used and a brief comment on the role of the regularised window).