Does the Kochen-Specker theorem rule out CSD?

The short answer

The Kochen-Specker theorem is the quieter sibling of Bell's. It shows you can't assign definite answers to all possible quantum measurements at once, independent of which experiment is actually performed, as any such table of answers contradicts itself, and any theory claiming a definite underlying reality has to reckon with it.

The reckoning is the same as with Bell, and it isn't evasion. The theorem's target is non-contextual assignment, meaning answers that don't depend on the measurement context, the actual physical arrangement doing the asking, so a theory whose outcomes depend on that context is outside the theorem's scope, at the declared cost of accepting the dependence.

CSD accepts the dependence and then does something the usual discussion doesn't. It makes the context a formal object with its own data, so "the outcome depends on the context" is a definition you can compute with and not a slogan.

The longer answer

In CSD a measurement context is a field of rates on the base of the arena, the space of quantum states, and it's the apparatus's own data. The outcome basins, the regions of the arena whose points lead to each outcome, are built from it, and distinct contexts genuinely induce distinct partitions of the arena, which is exactly the dependence Kochen-Specker demands of a surviving theory. The corpus proves the obstruction side too, in its own frame, as no global context-independent assignment is compatible with the exhibited contextual statistics, and the Mermin- Peres construction supplies the finite-dimensional contradiction.

One clarification comes from the analysis of where contextual structure lives. For systems of dimension three and above, the base-only construction fails, and that base-only failure isn't a corollary of Kochen-Specker, as CSD's partitions are contextual, so the classical no-go theorems don't apply to them. It's a separate constraint, coming from covariance and positivity, argued on its own.

What is actually proved

The contextuality tier is the global-assignment obstruction in the C1 chain, the Mermin-Peres square's contextuality witness, and the context-indexed outcome map machinery with its definitional separation, with no Fine-theorem shortcut assumed.

The N >= 3 fibre-placement analysis is explicitly distinguished from Gleason and Kochen-Specker in the source, and it's short of a no-go in its own right.

Related entries

• Kochen-Specker theoremThere's a finite list of directions in space that admits no consistent yes-or-no labelling, so contextuality follows by pure counting, with no experiment, no statistics and no separated particles.
• 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.
• Measurement contextA measurement isn't a question put to the quantum state, as it's a piece of apparatus, and the apparatus brings its own way of dividing the world into outcomes.
• 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.
• Gleason and Busch theoremsThe corpus proves the standard route to the Born rule rather than borrowing it, and CSD's own derivation never uses it, so the two routes to quantum probability are genuinely independent.