User blog:DrCeasium/The value of Rado's sigma function for 5-state TMs

Hi everyone, I'm back from the dead (again...), no promises about how long I'll stay active this time. I've seen some comments about FAN and stuff that people have made recently, you could well be right, I haven't really looked at any of my array stuff for quite a while.

Anyway, the reason for this post (as you can tell from the title) is to tentatively say I think I've proved all the hardly non-regular TMs run forever, so showing that $$\Sigma(5)=4098$$ and $$S(5)=47176870$$. I'm still in the process of writing it up, and it's not finished yet; some of the 'proofs' are still just collections of ideas, but I'm pretty confident I can stick them all together.

The reason that I'm posting this before I've actually finished sorting all the proofs out is that hopefully, this will encourage me to actually get on with finishing it, seeing that I've now said I think I can. If anyone's interested, I'm very happy to share the progress I've made with writing it all up so far (which is probably full of errors, typos and more).

Most of the proofs are fairly standard, just on a larger scale, but there are a few minor new (I think) ideas around as well.