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By ChatGPT* — 

What is the Cullinane diamond theorem? 
5/10/2023, revised as below on 5/15/2023

The Cullinane Diamond Theorem, also known as the Diamond Theorem, is a result in combinatorial mathematics proposed by Steven H. Cullinane. The theorem explores connections between finite geometries, algebraic structures, and combinatorial designs. 

The theorem is primarily concerned with four related structures:
 
1. Finite geometries: Specifically, the theorem relates to finite projective geometries over finite fields, such as projective planes and projective spaces. 

2. Vector spaces: The theorem connects finite vector spaces over finite fields to the aforementioned finite geometries. 

3. Boolean functions:* The theorem establishes relationships between the finite geometries and certain Boolean functions derived from them. 

4. Symmetry groups: The theorem involves symmetry groups associated with the finite geometries.
 
The precise details and implications of the Cullinane Diamond Theorem are beyond the scope of this response. It involves abstract algebra, group theory, combinatorial designs, and finite fields. The theorem has been the subject of various publications and research discussions in mathematical literature. If you are interested in delving deeper into the Cullinane Diamond Theorem, I recommend referring to the original works by Steven H. Cullinane and related research articles on the topic.

* With one revision by Cullinane: "Boolean functions" replaces "Boolean algebras." See (for instance) M. A. Harrison, “On the classification of Boolean functions by the general linear and affine groups,” Journal of the Society for Industrial and Applied Mathematics  1964 12:2, 285-299.