Hidden variables

In plain terms

Here is the problem. If the quantum state describes knowledge rather than the world, there has to be something the knowledge is about -- an underlying state of affairs, definite whether or not anyone looks. Theories that supply one are called hidden- variable theories, and a famous sequence of theorems is widely reported to have ruled them out.

The reports are wrong, in an instructive way. What Bell and his successors actually ruled out are the well-behaved hidden-variable theories: the local ones, and the ones assigning values independent of measurement context. Hidden variables survive -- at the stated price of locality and non-contextuality.

That is not a loophole. It is the theorem's actual content. Bohmian mechanics has been paying the price since 1952, and remains the standing proof that the reports of death were exaggerated.

In CSD

The constraint surface is a hidden-variable theory in the technical sense, and the programme says so out loud rather than hoping nobody asks. It is contextual and non- local -- exactly the two properties whose absence the theorems forbid -- and it proves the relevant obstructions in-house rather than citing them, since a reconstruction resting on trust in the theorems that constrain it would be oddly built.

Two standard misreadings, both worth killing. First: CSD is not a repair of quantum mechanics. It reproduces the same predictions at leading order; candidate departures are recorded as owed by the papers, not claimed. Second: the quantum state is NOT the hidden variable. The state is the summary. The hidden variable is the point of the constraint surface underneath -- which is why the state can be epistemic without the theory being about nothing.

Mathematically

No product partition of a shared hidden-state space reproduces the singlet correlations, at any setting pair; likewise GHZ. Proved over arbitrary measurable state spaces, so the constraint hits the class, not one construction.

The positive half is also in the corpus: an explicit contextual, non-local assignment that does reproduce the singlet. Together the pair delimits the viable region from both sides -- what cannot work, and one thing that does.