Cutoff for the Overhand Shuffle

We study the overhand shuffle with a fixed cut probability $p\in(0,1)$. In the packet-reversal convention, each gap is cut independently with probability $p$, and each resulting packet is reversed in place. We prove total-variation cutoff at \[ \frac{p^2}{2(1-p)π^2}\,n^2\log n. \] The lower bound