The Kochen Specker theorem says that hidden variable theories must be contextual. I'm not seeing anything in the definition of Bohmian mechanics that makes the hidden variable variable assignments dependent on the measurements. Bohmian mechanics seems to revolve around the Newtonian idea that hidden variables are assigned irrespective of measurements, and measurements simply reveal their values, thereby solving the measurement problem..
Bohmian mechanics treats $|\psi (x, y, z) |^2$ as a classical probability distribution, being acted upon by a classical potential $V$ and a quantum potential $Q$. There is some position hidden variable that this probability distribution describes.
This is sufficient to explain all quantum mechanical experiments involving a position measurement. But so far, this does not explain energy or momentum measurement probabilities. One solution can be to add this as a postulate:
If the pilot wave, corresponding to an ensemble, is $|\psi\rangle$, then as the system reaches the "Born equilibrium", each particle settles into a hidden variable state $a$ of observable $A$ with probability $|\langle a|\psi\rangle|^2$, where $|a\rangle$ is an eigenstate of $A$
Does Bohmian mechanics really use the above postulate?
If it has this postulate, then it can explain all quantum measurement statistics. But then again, this postulates seems inconsistent because it violates the Kochen-Specker theorem. This postulate is simultaneously assigning hidden variables to non-commuting observables in a non-contextual (measurement independent) way
Does this mean that the Kochen Specker theorem rules out Bohmian mechanics?