This is a continuation of the preceding two threads here on the polymath1 project, which are now full.  We are closing on on the computation of the sixth Moser number – the size of the largest subset of the six-dimensional cube $\{1,2,3\}^6$ that does not contain any lines: it is either 353 or 354, and 354 looks close to being eliminated soon.

Besides this, the nominal purpose of this thread is to coordinate the writing of the second paper of the project.  In addition to incorporating whatever results we get from the six-dimensional Moser problem, a lot of work still has to be done on other sections of the paper, notably the higher k component and the component on Fujimura’s problem, as well as the appendices.