Diophantine approximation and the Mass Transference Principle: incorporating the unbounded setup

The paper proves the exact formula dim_H W_d(Ψ) = sup_{t∈U(Ψ)} min{ min_{i∈L(t)} ζ_i(t), #L(t) } under the usual monotonicity hypothesis via an ‘unbounded’ rectangles-to-rectangles Mass Transference Principle (Theorem 2.1) and a careful upper–lower bound argument (Theorem 1.1) . The candidate solution arrives at the same formula. Its lower bound aligns with the paper’s unbounded MTP-based proof, while its upper bound uses a different route (subsequence power-law comparison and a slicing argument), rather than the paper’s truncation-plus-bounded-WW reduction . Minor caveat: the candidate asserts Rynne’s formula also for arbitrary subsequences Q; this independence-of-Q is not used by the paper and is not needed for the candidate’s argument (one can bound via inclusion into the all-denominator limsup).