For any particle at any stage of calculations the LSA keeps record of only two events: an old, already processed committed event, which comprises the committed event time stamp, the particle state (including position and velocity), and, perhaps, the "partner" which could be another particle or boundary identification, the one with which the particle collided in the past, and a new event proposed for a future processing with a similar set of parameters. The new event is not committed. The maximum of the committed old event times must never exceed the minimum of the non-committed new event times.