Source
Barbosa, Karvonen and Mansfield, Closing Bell (LIT-845, arXiv v2), §6.2, as read in NOTE-650. The paper states the adaptive analogue of its Theorem 44 and gives no proof.
What is asserted
THEORY-174 holds the non-adaptive statement, re-derived: a convex map between model sets is induced by a mixture of non-adaptive procedures exactly when some non-contextual model of the hom scenario [S, T] that satisfies its predicate induces it. §6.2 asserts the same for adaptive procedures, in which the source measurements an agent makes may depend on outcomes already seen, as in the comonadic simulations of LIT-847.
What this does not say
- That the non-adaptive proof carries over. Theorem 40, the characterisation of deterministic procedures, does not transfer to adaptive ones, because its key lemma (Lemma 39, least supports) fails for them (§6.2). Whether the short argument for Theorem 44 survives depends on how the adaptive hom scenario is defined, which the paper sketches without detail.
- Anything about the preorder. LIT-847 Theorem 20 shows adaptive simulation is the same preorder as convertibility by free operations (THEORY-720). That orders models; it does not say which maps are simulations.