I will start with a small digression about sine-Gordon model in low dimensional systems and the Berezinskii-Kosterlitz-Thouless (BKT) phase diagram. Then I will move on to introduce the material, with its long history that spans over the last four decades. It belongs to a family of purple bronzes, whose other members were early on shown to be Peierls-CDW compounds, while the physics of this Li-compound has remained elusive. From the beginning of 21st century experimental evidence has been mounting, indicating that it may be a rare realization of Tomonaga-Luttinger liquid in a solid state material. However, its lowest energy physics does not obey the canonical picture and the origin of a mysterious upturn of resistivity was understood only few years ago .
Then I will present our most recent findings that directly probe the parent state of superconductivity . We were able to show that the Li0.9Mo6O17 is in fact in the higher symmetry state, right on the edge of Mott insulating region in the BKT picture. I will explain how the specific properties of Li0.9Mo6O17 enabled us to measure directly the BKT renormalization group flow and what conclusions we were able to draw from that.
 J. Lu et al., Sci. Adv. 5, eaar8027 (2019).
 P. Chudzinski et al., Science 382, 792-796 (2023).