Measurement context

In plain terms

Here is the problem. Quantum mechanics is contextual: you cannot assign answers to all possible measurements at once, only to the ones an actual arrangement of equipment can co-ask. So "the measurement" is never just an observable on paper -- it is a physical context, and which context is in place matters to what can happen.

CSD takes the context seriously enough to give it a data type. A context is the information the apparatus actually contributes: for every possible state of affairs, a set of outcome rates. Fix the context and the outcome regions are fixed; change the context and a genuinely different partition applies.

That is the referee's-rulebook picture again: the rulebook belongs to the referee, exists before the match, and does not consult the players.

In CSD

Formally a context is a rate field on the base of the arena: a measurable, simplex-valued assignment of outcome weights to each ontic base point. The preparation plays no part in the assignment -- that is the A7 requirement, and the corpus's basins are built from the context's field alone. The canonical context reads its rates off the moment map, so even the rates are geometry rather than bookkeeping.

Contextuality then has a precise home: distinct contexts induce distinct partitions, and the no-go theorems against context-independent global assignments are proved in-corpus, alongside the positive witness showing a contextual model reproduces the singlet statistics in full.

Mathematically

ContextField: rate functions p -> Fin N -> R, measurable per outcome, nonnegative, summing to one at every point. The induced basins are measurable and pairwise disjoint with Born-weight epistemic probabilities; the canonical instance takes rate := momentMap with measurability supplied by the moment-map infrastructure.