Woah, 
.
The GGT algorithm min-cut based algorithms are effectively finding a subset x which maximizes
\operatorname{fee}_x - \lambda \operatorname{size}_x
for a given existing solution S with feerate \lambda. In order words, it maximizes
\operatorname{fee}_x - \frac{\operatorname{fee}_S}{\operatorname{size}_S} \operatorname{size}_x
which, given that \operatorname{size}_S is a constant in this context, is the same as maximizing
\operatorname{fee}_x\operatorname{size}_S - \operatorname{fee}_S\operatorname{size}_x
Which is what I’ve called q(x, S) in the spanning-forest writeup, the quantity being maximized when performing chunk splits…