Minimal families realized by position comparisons

Determine whether the comparison of positions in a box realizes the minimal family D6, and determine which of D6 and D7 is produced by Theorem 2(b) from a given dense sequence.

Background

The paper shows that the comparison of positions in a box realizes the canonical minimal families D3, D4, and D7, while the full classification of NIP observables also involves D6. The authors explicitly ask whether D6 can arise from the position-comparison observable and whether the classification theorem selects D6 or D7 for a specified dense sequence of preparations.

References

Does it realize $D_6$? Which of $D_6$ and $D_7$ does Theorem~\ref{thm:orders}(b) produce from a given dense sequence?

— Classification of bipartite observables II: NIP observables and the Todorcevic trichotomy  (2610.12908 - Dueñez et al., 9 Oct 2026) in Section Questions, item 2