Finiteness of degree-2n-3 reduced models

Establish whether, for every n≥3, the number of reduced one-dimensional discrete models in Δ_n of degree 2n−3 is finite, equivalently determining whether all such reduced models are fundamental.

Background

The paper notes that the number of reduced models in Δ_n of degree 2n−3 is finite for n=3,4,5,6, in which cases the corresponding reduced models are fundamental. It then proposes extending this observed finiteness phenomenon to every n≥3. The authors leave this as a conjectural question while proving instead that, for n≥4, non-fundamental one-parameter families occur at degrees at least 2n−4.

References

Another conjecture concerns the number of reduced models in $\Delta_n$ of degree $2n-3$. By Table~2, this number is finite for $n=3,4,5,6$, and therefore the corresponding reduced models are fundamental. A natural conjecture is that this is true for all $n\ge3$.

— One-dimensional Discrete Models of Maximum Likelihood Degree One  (2507.18686 - Améndola et al., 24 Jul 2025) in Section “Enumerating Fundamental Models,” paragraph beginning “Another conjecture concerns the number of reduced models”