Remark: What the ball countermodel does and does not say

The two countermodels witness different failures of inference. A Euclidean-ball section is compatible with scheduler consistency. It is not, merely by being a ball, a non-Lorentzian continuum cone: indeed,

A discrete one-step section and its generated reachability structure must therefore be distinguished from this full continuum homogenization.

The orthant supplies the direct non-Lorentzian cone obstruction in dimension at least three. The statement “ball and orthant are countermodels” is shorthand for the separately specified nonimplications in En08-A, not a claim that every cone over a Euclidean ball is non-Lorentzian CheungEn08A (prop:ball, prop:orthant).