A Dimensional Mass Transference Principle from Balls to Open Sets and Applications to Dynamical Diophantine Approximation

The paper proves the large intersection property via a detailed, Euclidean, measure-construction argument that crucially uses the quasi-self-conformal reference measure ν and Besicovitch covering to control disjointness and content inside selected families (Cor. 2.6; Sec. 3.1–3.2). It then applies a general criterion for G^s(X) (Theorem 2.3) to conclude limsup E_n ∈ G^s(X). By contrast, the model asserts a stronger, different mass-transference principle for arbitrary sets E_n (not just balls) in a general metric space, and drops ν entirely, citing Eriksson–Bique (2024) without demonstrating that their result covers this general “balls-to-sets with content lower bounds” setting. The model also replaces the paper’s exponent dim_H ν by δ without justification. Hence the model’s argument is unsupported under the stated hypotheses, while the paper’s is correct.