Conjecture on the number of quadruple points in the example

Let $f$ be the map-germ considered in the paper, and let a stable perturbation of $f$ have quadruple points. Quadruple-point count conjecture. The number of quadruple points is $8970$. The paper explains that establishing this would require proving a conservation principle for the relevant Fitting-ideal module; because the required stable unfolding has at least 40 parameters, the authors can only conjecture the count.