Conjecture on Benford behavior of perimeters in rectangle fragmentation

Consider a rectangle undergoing an unrestricted fragmentation process, and let its sub-rectangles be the resulting pieces. The perimeter of a sub-rectangle is the sum of its side lengths, and Benford behavior means that these perimeters converge in significand distribution to Benford's distribution.

Rectangle-perimeter conjecture. The perimeters of the sub-rectangles from a rectangle undergoing an unrestricted fragmentation process converge to Benford behavior.

The conjecture is motivated by simulations and is presented as a concrete lower-dimensional analogue of the paper's full-dimensional volume results. The supplied text gives no resolution status.