No-signalling

In plain terms

Here is the problem. Entangled particles show correlations that no local story explains, and the first thing every newcomer asks is whether that lets you send messages faster than light. Quantum mechanics says no. A programme reconstructing quantum mechanics had better say no as a theorem, not as an apology.

Here it is a theorem, twice over. At the level of composite arenas: disturb one sector however you like -- any local operation -- and every observable of the other sector keeps exactly the same value. Not approximately: the change cancels identically. And at the level of the Bell model: the explicit contextual model that reproduces the singlet statistics has provably invariant remote marginals.

Correlation without signalling is not a tension to manage. It falls out of what local operations can and cannot touch.

In CSD

No-signalling in CSD is a statement about operator support, not a constraint imposed on probabilities: a kick supported on the right modes commutes past every left-supported observable, so the left statistics are untouched -- an instance of the arena's locality statics, holding for all states because it never mentions the state.

The Bell-model version matters separately: contextual models are exactly the kind critics suspect of hidden signalling, so the corpus proves the operational no-signalling predicates for its exhibited model rather than gesturing at them.

Mathematically

composite_no_signalling: on the composite field arena, conjugating by any unitary supported on one sector leaves every observable of the other sector's subalgebra exactly invariant, for every composite state. The contextual-model version proves remote marginal invariance for both wings -- one shared measure across contexts, which is measurement independence stated in-module. Both are foundational-triple-only.