A single-variable proof of the omega SPT congruence family over powers of 5.

In 2018, Liuquan Wang and Yifan Yang proved the existence of an infinite family of congruences for the smallest parts function corresponding to the third-order mock theta function . Their proof took the form of an induction requiring 20 initial relations, and utilized a space of modular functions isomorphic to a free rank 2 -module. This proof strategy was originally developed by Paule and Radu to study families of congruences associated with modular curves of genus 1.