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Aug 18, 2023 at 1:21 comment added Alison Miller Glad that was helpful! I don't know of any more recent papers looking at Bhargava cubes from the moduli stacks perspective, but I'm also curious what the precise relationship is! The paper "Rings of small rank over a Dedekind domain and their ideals" by Evan O'Dorney generalizes all Bhargava's composition laws to a general Dedekind base ring in place of Z, but I don't know anything that studies the moduli problem generally. Great question!
Aug 17, 2023 at 23:38 vote accept skd
Aug 17, 2023 at 23:38 comment added skd Thank you very much! Having these references is extremely helpful; following Bhargava's references led me to Gelfand-Kapranov-Zelevinsky, which explains that this discriminant in Bhargava's paper is the Cayley hyperdeterminant. I'm still curious to know if there's some relationship between these stacks, but maybe this is answered in one of the many papers citing Bhargava and Wood.
Aug 16, 2023 at 17:49 history answered Alison Miller CC BY-SA 4.0