On the dimension of arcs in mixed labyrinth fractals

The paper rigorously constructs mixed labyrinth fractals whose every arc has prescribed box-counting dimension δ ∈ [1,2], proving δ=2 via snake cross patterns and the general case via carefully blocked repetitions of consecutive snake-cross widths; the reduction from exit–exit arcs to arbitrary arcs uses the standard arc-construction in dendrites. The candidate solution’s core construction (its “4B” block/quotient scheme) is essentially the same idea and is correct. However, it overstates a general exit–exit equality (uses a limit rather than limsup/liminf in general) and presents an unnecessary and flawed fixed-width mixing (“4A”). These issues are peripheral to its main, correct construction.