I'm writing up some math results developed on LW as a paper with the tentative title "Self-referential decision algorithms". Something interesting came up while I was cleaning up the Loebian cooperation result. Namely, how do we say precisely that Loebian cooperation is stable under minor syntactic changes? After all, if we define a "minor change" to program A as a change that preserves A's behavior against any program B, then quining cooperation is just as stable under such "minor changes" by definition. Digging down this rabbit hole, I seem to have found a nice new reformulation of the whole thing.
I will post some sections of my current draft in the comments to this post. Eventually this material is meant to become an academic paper (hopefully), so any comments on math mistakes, notation or tone would be much appreciated! And yeah, I have no clue about academic writing, so you're welcome to tell me that too.