The seven-neuron conjecture for locally good codes

A code is locally good if every link of every codeword is contractible. Seven-neuron conjecture. Every locally good code on at most $7$ neurons is open convex or closed convex. The paper gives an example on $8$ neurons with these local properties that is neither open convex nor closed convex, and asks whether fewer neurons can support such an example; the supplied text does not establish the conjecture's resolution.