A clean prominence list criterion corresponds to the minimum prominence a peak has based on the maximum possible saddle elevation. A clean list will only contain peaks that are guaranteed to meet or exceed the chosen cutoff prominence. It results in an incomplete list since other peaks might exist that in truth have the desired cutoff prominence. However nobody can dispute the claim that any peak on the list has in truth at least the required cutoff prominence value.
A mean prominence list criterion is the average prominence a peak has based on interpolating the saddle elevation halfway between the latter's minimum and maximum possible values. Mean prominence has been called "interpolated prominence".
A maximum prominence list criterion corresponds to the greatest prominence a peak has based on the minimum possible saddle elevation. A maximum prominence list might contain peaks that do not in truth have the chosen cutoff prominence. However the resulting list has the advantage that a peakbagger who completes this list is guaranteed to have climbed all peaks that could possibly in truth have the chosen cutoff prominence.
There are sound statistical arguments for why a mean prominence list criterion is the definition of choice.
Clean and minimum prominence list criteria result in peaks at the list's bottom,
the so-called "gray zone", that are correctly placed (either on or off the list) only roughly 50% of the time.
For clean prominence, 45-50% of the peaks will be incorrectly left off the list.
For minimum prominence, 50-55% of the peaks will be incorrectly placed on the list.
In contrast, use of a mean prominence list criterion results in 75% of gray zone peaks being
correctly placed as either on or off the final prominence list.