The Dynkin-diagram conjecture for braid monodromy groups

Let $f$ be a singular function and let a Dynkin diagram encode its algebraic monodromy. Consider the braid subgroup associated to such a Dynkin diagram, allowing conjugation in the braid group. Dynkin-diagram conjecture. The braid monodromy group of a singular function coincides with the braid subgroup associated to a Dynkin diagram up to conjugacy. If true, this would give a description of braid monodromy groups in terms of Dynkin diagrams and would make them topological invariants despite their possible dependence on analytic invariants. The source states no resolution.