This is really interesting, but doesn't it presume that there's only one trading venue for each instrument, and that instruments aren't correlated?

You can make time discrete for a single auction, but the time between auctions still has to be continuous unless everything's traded in a single exchange, which can't in reality happen even if we want it to (and we probably don't).

As I understand it, most of the most dramatic HFT stuff is already targeting multi-venue trades or correlations.