Graph Iterated Function Systems and Fractal Tops

Grover Lancaster-Cole, Georgiana Lyall, Thomas Malcolm, Qiyu Zhou

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves S(Σ_top) ⊆ Σ_top (Lemma 4.2) and concludes that the closure of Σ_top is a shift space (Theorem 4.3) via continuity of S and Proposition 2.2; the candidate solution proves the same two claims with a near-identical minimality/invertibility argument and the same closure-plus-shift-invariance criterion. The differences are stylistic (use of Lemma 2.4 in the paper versus a direct minimality contradiction in the model), not substantive. Core hypotheses (invertibility of each f_i, existence of lexicographic minima, continuity of S, and that Σ is a subshift of finite type) are aligned with the paper’s setup.

Referee report (LaTeX)

\textbf{Recommendation:} no revision

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The specific results audited (shift inclusion for tops and closure as a shift space) are established with correct logic, appropriate hypotheses, and clear references. The candidate solution mirrors the paper's reasoning with only stylistic differences and no substantive gaps. The contribution is a sound extension from classical IFS to the graph-directed setting, with careful use of symbolic dynamics fundamentals.