From one 11 to another in four dimension

In this blog post I would like to relate two occurences of 11’s in four manifold theory: one is the 11 that appears in the gauge coupling constant in 4D YMs, which I have written about in \cite[???]; while the second is the famous 11 in the $\frac{11}{8}$ conjecture. I am going to sketch out a long argument (and NOT PROVEN AT ALL) showing show the physical 11 implies the second 11. This is based on Furuta’s proof of $\frac{10}{8}$ conjecture, which I will also give an argument that this should be able to strengthen to $\frac{11}{8}$, which of course many people thought off and is not currently shown.