# Phylogenetic complexity of the Kimura 3-parameter model

## TL;DR

This paper proves that the algebraic ideals of the Kimura 3-parameter phylogenetic model are generated in degree four, confirming a longstanding conjecture in algebraic statistics.

## Contribution

It establishes that the ideals for this model are generated in degree four, resolving a key conjecture by Sturmfels and Sullivant.

## Key findings

- Ideals are generated in degree four
- Confirmed a conjecture by Sturmfels and Sullivant
- Advances understanding of algebraic structure of phylogenetic models

## Abstract

In algebraic statistics, the Kimura 3-parameter model is one of the most interesting and classical phylogenetic models. We prove that the ideals associated to this model are generated in degree four, confirming a conjecture by Sturmfels and Sullivant.