This is a linkpost for https://www.arxiv.org/pdf/2508.16245

The grain of truth problem asks how multiple agents having consistent mental models can reason and learn about each other - recursively. 

With Marcus Hutter, Jan Leike (@janleike), and Jessica Taylor (@jessicata) , I have revisited Leike et al.'s paper "A Formal Solution to the Grain of Truth Problem" (AFSGOTP) which studies games between reflective AIXI agents and... further formalized it. 

The result is "Limit-Computable Grains of Truth for Arbitrary Computable Extensive-Form (Un)Known Games" (LCGOTACEFUG) which perhaps could have been called "A Formal Formal Solution to the Grain of Truth Problem." Our new paper has some new results, including:

•  An application to Self-AIXI which suggests an embedded version of AIXI. Since we have had these results unpublished for awhile, I have been implicitly leaning on these ideas for e.g. coming up with AEDT w.r.t. rOSI.  
• Reflective oracles with non-binary alphabets and explicit types for symbols 

...but mostly we just expand on various definitions and algorithms that were previously left implicit in AFSGOTP. Basically, our new paper LCGOTACEFUG  is a "journal version" of AFSGOTP. Except it is not published in a journal yet, because peer review is slow.

Who should read this?

• Anyone interested in reflective oracles and particularly reflective AIXI, who has not yet read previous works such as AFSGOTP, should probably just read our paper LCGOTACEFUG. It is more complete and hopefully the most legible introduction to the topic.
• Anyone who is actively doing research on reflective versions of AIXI

Errata: The proof of Theorem 45 should not say "with O-access."