The stabilizer conjecture for braid monodromy and algebraic monodromy

Let $f$ be a singular function, with braid monodromy group acting by the Artin representation on its algebraic monodromy homomorphism. Stabilizer conjecture. The braid monodromy group is the stabilizer subgroup of the algebraic monodromy homomorphism. This is an immediate proposed description of the braid monodromy group in terms of the algebraic monodromy; the source presents it as an educated guess for general functions, with no resolution stated.