With their "synchronize-local-clocks" approach, it doesn't.

They are using Lamport's algorithm to synchronize the clocks. However, Lamport's approach creates a _partial_ ordering, and to make that a _total_ ordering you need some mechanism to break "ties". For instance, the PID, or whatever.

The catch is that the relationship derived from this arbitrary tie-breaking mechanism has nothing to do with causality, and therefore the total order it imposes is only an artifact of the mechanism chosen.

Finding a tie-breaking mechanism that corresponds to the sending events is, in Lamport's own words, "not trivial".