Von Neumann derived value constraints from statistical constraints by assuming algebraic relations between values transfer into the statistics of measured values.

Despite the use of statistics, this reasoning crucially differs from von Neumann’s argument. Von Neumann had argued that algebraic relations between values should transfer into the statistics of the measured values, therefore the QM constraints on these statistics should have value constraints as their exact mirror images — which reasoning leads us to derive value constraints from statistical constraints (for arbitrary observables). Here, on the contrary, we derive a value constraint independent