The short answer is no. The reason is that the associative law
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does not hold excatly when finite precision computations are performed. On any computer MOSEK runs all computations are performed n finite precision.
The implication of that the associative law does not hold exactly is a reordering of the computations can lead to slightly different results.
Now MOSEK adapts itself to different hardware in order to improve performance. This usually has the implication that the ordering is reordered and hende different results may the results.