Boyer-Kassem et al.'s conclusion names a scope-limited retreat and an untested POVM fix as the quantum-like program's remaining escape routes

Boyer-Kassem, Duchêne & Guerci (2016, arXiv:1606.03430) do not present their refutation (claim-boyer-kassem-refutation-rejects-non-degenerate-and-degenerate-models, claim-conjunction-fallacy-order-effect-account-refuted-generally) as an unqualified end to quantum-like modeling of the conjunction fallacy. Their own conclusion names two live, unresolved escape routes.

The first is a scenario-restricted retreat: rather than claiming quantum-like models explain the conjunction fallacy in general, a future line of research could split scenarios by type ("AB" vs. "MA") and claim coverage only of a subset. The authors are explicit about the cost: "the quantum-like account would loose [sic] its generality, which was its strength." The second is a technical extension — replacing the standard projective ("Born rule") measurement structure with the more general Positive Operator-Valued Measure (POVM) formalism from quantum physics, "recently applied to quantum-like models of cognition." The authors flag this path as already facing "some new challenges like response replicability," and offer it as a research strategy to try, not a result they've obtained.

Neither route is described as closed, and neither is described as achieved. That distinction — a named, plausible repair path vs. a demonstrated repair — is exactly the gap the vault's open question tracks (question-quantum-cognition-conjunction-fallacy-fatal-or-scope-limit), and it's the gap the next claim in this cluster (claim-no-rebuttal-found-lebedev-khrennikov-targets-different-question) checks against the subsequent literature.