Claim, conventions, and source boundary

A finite event poset is not itself a vector-space cone. Accordingly, “the extracted order is Lorentzian” will mean the precise representation statement in Section sec:target, not a linear bijection from finitely many events onto ${\mathcal{L}}_m$.

The present convention uses a closed cone order. An open chronological relation would instead use $\mathrm{int}K$. Passing between these two relations requires an explicitly stated closure or boundary argument; it is not a notational identification.

operational languages. Process matrices, quantum combs, and multi-time process tensors provide different operational frameworks OCB,CDP,Pollock. They are possible languages for Stage 1, not interchangeable models and not hypotheses of a selection theorem in this note. A future choice must specify:

1. the finite party or slot set and the input/output Hilbert spaces;

2. the admissible preparations, instruments, interventions, and retained outputs;

3. whether the datum consists of exact complete maps, exact intervention probabilities, or finite statistical records;

4. the operational equivalence and relabelling conventions;

5. which relation is being extracted.

Finite parties do not necessarily mean finitely many admissible interventions. Conversely, finitely many observed event comparisons do not supply a continuum carrier.

convention. The Cheung references below identify unpublished manuscripts by their supplied identifiers, versions where available, and internal labels. A cited restatement is not an independent verification of the predecessor proof. En08-A is used for the obstruction; the cone classification is attributed directly to Ito and Lourenço. Other series references are documentary comparisons unless expressly identified otherwise.