Even though, below 3500′ the NYSDEC allows at-large camping, “closest camping” refers to the closest lean-to, designated (primitive) campsite, and/or state campground.
Every peak that is not a landmass/island high point is connected to a higher peak by ridges and has exactly one key col, which is the lowest pass on the highest ridgewalk leading to a higher peak
The Line Parent is defined as the first higher peak encountered from the given summit, following ridgelines past the key col.
Every peak on earth except Mount Everest has a NHN. Great circle, as-the-crow-flies distance is always used to find the NHN for a peak.