Tian on Nostr: I wonder if with 8 points there are actually at least three blocked. It's true in the ...

I wonder if with 8 points there are actually at least three blocked. It's true in the "main branch" of the argument (midpoints of AM and MB) and in the case of at least three points with same parity type. But can we have four pairs of points with same p.t. such that the four midpoints are two different points, without blocking any other?