originally, it was unknown whether any of these principles (or a subset thereof) was strong enough to derive all the constraints defining formula_111. this state of affairs continued for some years until the construction of the almost quantum set formula_182. formula_182 is a set of correlations that is closed under wirings and can be characterized via semidefinite programming. it contains all correlations in formula_110, but also some non-quantum boxes formula_133. remarkably, all boxes within the almost quantum set are shown to be compatible with the principles of ntcc, nanlc, ml and lo. there is also numerical evidence that almost quantum boxes also comply with ic. it seems, therefore, that, even when the above principles are taken together, they do not suffice to single out the quantum set in the simplest bell scenario of two parties, two inputs and two outputs.