Candidate A: process-matrix signalling data

Fix bases and use the unnormalized Choi operator

where ${}^{\mathsf{T}}$ is the full transpose in those bases. In this convention a process matrix $W$ assigns

Positivity and normalization for all admitted local instruments, including the required ancillary extensions, are part of process validity OCB.

Candidate A consists of $W$, the instrument-access declaration, and its unconditional signalling tests. The framework does not impose one global party order at the outset. This does not mean that every $W$ lacks definite order, nor that causal nonseparability selects a Lorentz cone.

The extracted object initially is a signalling relation. The phrase “the signalling partial order of $W$” is permissible only after an order theorem or a declared order-forming construction.