Just write a short informal email. If the person needs a long-winded polite email to answer, then perhaps you don't want to have to interact with them.

Well you can do it but we don't have any proof. We actually also ran alpha-DSBM with zero-variance noise, i.e. so really an "alpha-rectified flow": experimentally it does "work" but we have no proof of convergence for the procedure.

Yes the trajectories are not quite smooth as they correspond to a Brownian bridge and, as the variance of the reference Brownian motion of your SB goes to zero, you get back to the deterministic and straight paths of OT.

I personally read at least a couple of hours per day. It is not particularly focused and I might "waste" time but I just enjoy it.

Very nice paper indeed. I like it.

I couldn't speak for the following 3 days :-)