Last weekend I’ve had a look at the “undulation” effect at 1ns transition times and sure enough I was able to reproduce it on the SDG6052X, as demonstrated by the following screenshots. Yet it’ll turn out that’s not the whole story…
First the minimum pulse width of 3.4ns with 1ns transition times viewed on a fast scope at a timebase of 5ns/div. The reference traces are just there to demonstrate what this pulse looks like with 200MHz (blue) and 20MHz (orange) 1st order bandwidth limit. This further demonstrates that we really need a fast scope in order to properly characterize a beast like the SDG6052X:

Pulse_BWL_SDG6052X_1.5V_3.4ns_1ns
The same scenario at a faster timebase of 1ns/div just for closer inspection. We can see that the rise- and fall times of the SDG6052X are still pretty accurate despite the continuously changing waveform, aka “undulation”:

Pulse_BWL_SDG6052X_1.5V_3.4ns_1ns_Z
As we already know, this effect nearly ceases when reverting to the default 2ns transition times:

Pulse_BWL_SDG6052X_1.5V_3.4ns_2ns
The same “undulation” effect can be observed with wider pulses, like 10ns in the following example:

Pulse_BWL_SDG6052X_1.5V_10ns_1ns
And again, the pulse gets pretty clean with 2ns transition times:

Pulse_BWL_SDG6052X_1.5V_10ns_2ns
So far so good (or not), this has been nothing new. But when I needed a narrow pulse with fast transitions again the next day, things looked completely different. As can be seen, all of a sudden the shape of the pulse is now absolutely stable and as expected, average transition times got even faster with less standard deviation:

Pulse_SDG6052X_1.5V_A10dB_3.3ns_1ns
The same is true for the wider 10ns pulse:

Pulse_SDG6052X_1.5V_A10dB_10ns_1ns
Finally a cursor measurement in order to confirm the automatic rise time measurement of 970ps:

Pulse_SDG6052X_RT_1.5V_A10dB_10ns_1ns
So it looks like the SDG6000X behaves differently (depending on its mood) every other day and I suspect some incomplete initialization, which Siglent should be able to fix eventually. At least my test indicates that the issue should be easily fixable.
Btw, I also looked at the Sync to Output jitter and was unable to reproduce it at 1MHz. Yet the ~3.3ns jitter is certainly there at most other frequencies.