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How many mass/school shootings have been committed with a pistol using a “stabilizing brace”? Or even just how many firearm-related homicides in general have been committed with one?
I give it 3 months before the SC tells them no. >

Under Bruen & Heller, this should not hold up in court, but it could take years.  
However, considering that the ATF changing an interpretation of a definition (that conflicts with their previous interpretation of that same, unchanged definition) could make millions of people felons I think an injunction is likely.