This paper is apparently a continuation of the author's programme of `quantizing' the entire foundations of mathematics, in which he turns his attention to topos theory, and in particular to the construction of a classifying topos for the theory of rings, which he takes as his goal (though it is never made clear why the theory of rings should be singled out for such particular attention). It is heavily dependent on the author's previous papers: most of the definitions and terminology which he uses are explained in the paper (with the key exception of that of a `manual of Boolean locales' -- or rather, the purported definition of this concept on page 2560 is circular), but a reader who is not already familiar with the author's notation will find it fairly heavy going. (In particular, he introduces a lot of nonstandard notation and terminology for 2-categorical concepts -- he appears to be familiar with much of the literature of topos theory, but not with that of 2-category theory.) The paper consists very largely of definitions -- it is somewhat disconcerting to arrive at a section headed `The first preliminary theorems' within three pages of the end of the paper -- and there is no clear motivation given for the development of the theory (perhaps the motivation is contained in the author's previous papers, which the reviewer has not seen). Insofar as the reviewer has been able to understand the concept of a `manual of Boolean locales', it appears to be somewhat similar to that of a `lamination' introduced nearly twenty years ago by \textit{L. N. Stout} [Manuscr. Math. 28, 379-403 (1979; Zbl 0409.03039)] with a similar (but more modest) objective. Roughly speaking, a manual is a certain sort of diagram of Boolean locales, and one then considers `empirical structures' which are various sorts of structures fibred over the corresponding diagram of Boolean localic toposes. The objective of the paper is to show that many of the constructions one is accustomed to carry out on structures within (or fibred over) a single topos can be carried out in this more general context.