ON DIRICHLET NON-IMPROVABLE NUMBERS AND SHRINKING TARGET PROBLEMS

The paper proves that dim_H E2({z_n},B) = limsup s_n with s_n built from three pre-dimensional series, via a careful two-case covering for the upper bound and a pressure/Cantor-measure construction for the lower bound. The model’s solution independently reconstructs the three covering mechanisms in the tail coordinate and performs a Moran-type lower bound via quasi-multiplicativity/Frostman. The core combinatorics (continued-fraction cylinders, inverse-branch scaling ≍ q_n^{-2}, and the three families leading to s_{n,1}, s_{n,2}, s_{n,3}) match the paper. The model, however, contains a sign/inversion slip when stating (T^n)' (it writes the inverse-branch derivative as the forward derivative) but then consistently uses the correct scaling for pullbacks; this is a minor correctable issue that does not affect the argument’s substance.