Is CSD a hidden-variable theory?

The short answer

"Hidden-variable theory" is a technical classification and not an insult. It means a theory in which something definite underlies the quantum state, so the state is a summary of a more detailed reality, and CSD has exactly that, the arena, its underlying state space, and the one real trajectory through it. So the honest answer is yes, with the classification's fine print read aloud.

The fine print is the no-go theorems, and they don't say what the one-line summaries claim. Bell's theorem rules out local hidden variables, those in which a choice made far away can never affect an outcome here, and the Kochen-Specker theorem rules out non-contextual ones, those in which every measurement has a fixed answer regardless of which other measurements are made alongside it. Surviving both means being contextual and letting correlations exceed what locality permits, which is precisely the shape CSD has, on purpose.

One error is worth avoiding, as the quantum state isn't the hidden variable. The state is the visible summary, and the hidden variable is the point of the arena beneath it, including the fibre coordinate, the part of the underlying state no quantum state determines.

The longer answer

The corpus proves the constraining theorems itself rather than citing them. No way of splitting a shared space of hidden states into a part for each particle can reproduce the singlet correlations, the strongest correlations of a paired two- particle state. No single context-independent assignment of outcomes survives contextuality. And the GHZ and CGLMP obstructions, named after Greenberger, Horne and Zeilinger and after Collins, Gisin, Linden, Massar and Popescu, which are further Bell-type results for more than two particles and for measurements with more than two outcomes, hold at general dimension. The corpus also proves that the survival is genuine rather than verbal, as the contextual model that reproduces the singlet table exists as a constructed object.

Where the correlations exceed locality, signalling still provably doesn't occur. Locality of operations holds exactly, as an intervention far away moves no local statistic, and that's the physically load-bearing half of locality, and the one experiments enforce.

What is actually proved

no_product_partition_realises_singlet and its GHZ companion over arbitrary measurable state spaces, the global-assignment obstruction and the contextual witness in the C1 capstone, and composite_no_signalling, exact for all states.

The Kochen-Specker-adjacent contextuality machinery of the Mermin-Peres square is also in-corpus.

Related entries

• Hidden variablesThe no-go theorems don't kill hidden variables, as they price them, and CSD reads the price tag and pays it.
• ContextualityFor some sets of quantum questions no consistent answer sheet exists at all, and CSD's response is to stop demanding one answer per question and to say instead what the answer depends on.
• Does CSD violate Bell's theorem?No. Bell's theorem stands, CSD proves its own versions of it, and CSD escapes its conclusion by the one route the theorem itself leaves open, measurement outcomes that depend on the measurement context, paid for openly.
• How does CSD differ from Bohmian mechanics?They're cousins rather than twins, as both theories pay the price the no-go theorems demand of any deterministic account, but Bohmian mechanics postulates its equilibrium distribution where CSD proves its measure unique, and the arenas underneath the two are different kinds of object.
• Does the Kochen-Specker theorem rule out CSD?No. The Kochen-Specker theorem forbids giving every possible measurement a fixed answer independent of which experiment is actually performed, and CSD assigns outcomes through the measurement context by construction.