`Π` not evolving in terms of size until first target difference at height 32,256 = 16 * 2,016

2,016 being the Bitcoin epoch length.

The issue comes from the fact that score(llbracket(CStar, 1)) >= previous_score uses score which takes into account the targets which as explained in the title doesn't change until a given height.

Replacing >= with > solves the issue but, as discussed with @l22mille on this whiteboard, >= seems preferable.

It seems that fundamentally the issue comes from the fact that as the new incoming block drops the oldest one, we can't create higher levels except if all the 2 * m blocks are from a higher level which occurs with probability 1 / (2 ** (2 * m)). So contrarily to Mining in Logarithmic Space, we have to keep somewhere higher level blocks than current highest level with 2 * m blocks. We should firstly investigate how they consider this aspect before doing so.