The central mystery of quantum mechanics (according to Feynman)

[bhobba]

Is that what you mean that for contextual hidden variable the sum of average could be different than the average of the sum ?

No.

It's simple.

If you have a look at Gleason you will see its watertight if the measure defined on a projection operator depends only on the operator itself and not on other operators it may be part of in a resolution of the identity. The only out is if that's not the case. It's not the case for some hidden variable theories.

I have zero idea where you are getting your other equations from, what they mean, what the terms mean, context or anything.

Please detail exact context and meaning.

They look like some equations I vaguely remember from papers on hidden variables, but you need to detail exactly what the terms mean and their derivation. A concern I have is when you say 'I suppose such and such is a contextual expression' it indicates you do not know what the terms mean. It's very hard for someone to figure out what you are driving at if that is the case.

Thanks
Bill