[ggm]

Monotonically rising time with a negative leapsecond...

[repsilat]

Actually the negative leap second is "more monotonic" than the regular one. Normally a leap second adds an extra second (58, 59, 60, 00), but a negative leap second skips one (58, 00).

Uniquely specifying the four times in the first sequence as UNIX timestamps isn't strictly possible, but it is possible with negative leap seconds.

[contravariant]

Now this is going to sound crazy but what if we just extend the year by a few seconds by default? Then we can just skip seconds as needed.

[ggm]

phew!