Does CSD violate Bell's theorem?

The short answer

Bell's theorem isn't violated by any theory that matches experiment, and CSD is no exception. What the theorem forbids is a specific package, hidden variables, meaning definite underlying states beneath the quantum description, that are both local and context-independent. Local means a choice made at one place can't affect an outcome at a distant place, and context-independent means a system's answer to a measurement doesn't depend on which other measurements are performed alongside it. Bell showed that any such package must obey certain numerical limits, his inequalities, and quantum experiments break those limits. The theorem survives that breaking, as it's precisely the proof that no local, context-independent package can produce what the experiments show.

CSD reproduces the quantum violations, and it respects the theorem by not being in the forbidden class, as its outcome assignments depend on the measurement context. That isn't a loophole, as it's the price the theorem itself names, and the programme pays it in the open.

The distinctive part is that CSD doesn't ask you to take any of this on trust. The obstruction theorems, the results that rule out the forbidden package, are proved inside the corpus, and so is the half most discussions skip, an explicit contextual model that actually reproduces the statistics of the singlet, the maximally correlated two-particle state that's the standard test case for Bell's theorem, in full.

The longer answer

The corpus carries both directions as a single machine-checked capstone result. The negative direction has two parts. No way of splitting a shared space of hidden states into one part for each particle, with each part deciding its own outcomes, can reproduce the singlet correlations, and no single assignment of outcomes to all measurements at once, independent of context, is compatible with the correlation table the model reproduces. These are Bell-type obstructions proved in-house, for the whole class of such models rather than for a convenient strawman.

The positive direction exhibits an explicit family of shared-context outcome maps on the corpus's own arena, measurable in the sense needed for probabilities to make sense, that reproduces the complete singlet table, the statistics of each side alone and the correlations between the sides, at every choice of settings. The model is proved to be no-signalling, meaning neither side can learn anything about the other's choice of setting from its own statistics, and measurement independence, the assumption that the distribution of hidden states doesn't depend on which settings are chosen, is named as a premise and verified for the model rather than quietly assumed.

Evading Bell is cheap until the model is on the table, and the point of the capstone is that the model is on the table. Since October 2026 the violation is proved of records as well as of outcome maps, as a two-wing experiment on the programme's own space reads each wing's result off a region of that space and reaches the quantum maximum for those regions. Locality still enters as an assumption about how the apparatus couples to each wing, so the result widens what the model covers without touching what the theorem demands.

What is actually proved

The capstone c1_singlet_contextual_capstone states existence and obstruction in one statement, and the supporting results are no_product_partition_realises_singlet over arbitrary measurable spaces, the GHZ and CGLMP obstructions at general dimension, remote marginal invariance for both wings of the exhibited model, and the CHSH and Tsirelson analysis in which the inequalities sit.

All of these are proved from the foundational axiom triple alone.

Related entries

• Bell and CHSHNo pre-written answer sheet for all four measurement settings can match what a singlet pair of particles does, and the corpus proves this as a theorem about every possible answer sheet.
• Singlet contextual modelOne machine-checked theorem settles both halves of the Bell question, as an explicit model in which outcomes depend on the measurement context reproduces the singlet pair's statistics in full, and no assignment that ignores the context can.
• No-signallingNothing done to the far wing of an entangled pair changes the statistics seen at the near wing, and CSD proves this exactly, for every state, entangled ones included.
• Is CSD superdeterministic?No. In CSD's Bell model the distribution of hidden states is provably the same whatever settings the experimenters choose, and the escape from Bell's theorem runs through outcomes that depend on the measurement context and not through settings arranged in advance.
• Is CSD a hidden-variable theory?Yes, in the technical sense, as something definite underlies the quantum state in CSD, and the programme openly pays the two prices the no-go theorems demand, dependence on measurement context and correlations beyond what locality permits.