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[8x11] Help me understand this Minox LX issue

That's a common assumption. If that were true, why would they cut it down to 9.25mm?

Not trying to argue as this is just fun speculation, but it is possible that they started with the 9.5mm spec then found problems with it later. Makes sense that they started with a readily available film size vs. making their own. One would have to find a roll of film from the very beginning to really know the answer to all that (or find the original design specs). .25mm ain't much in the vast scheme of things but inside a Minox cassette it is a lot. If it ended up that even though they designed it for 9.5mm, if there were issues then it would be easier to make the film smaller than change the design of the camera. Minox film has varied over the years too. Some older film is wider than more modern film. Again, .25mm isn't much really. I suppose I could measure some old rolls I have laying around I haven't gotten around to using yet. Might be interesting to see but I've never done it.

I suppose one could try to cut a roll of 9.5mm film then put it in an old Riga and see if it works or jams. Of course this is all just academic speculation since it doesn't really matter to us in the modern world. 9.25mm works fine for all the cameras.
 
It could also be that they designed it with an "acceptable tolerance" in mind (especially if people were going to slit their own film), with something like 9-9,5mm being the allowable sizes (just as an example), and just aimed for the middle of that spec.

That way, at least, there wouldn't be too much issues if someone cut their film without using Minox's own tooling, or if the width on a roll wasn't perfectly consistent. It was designed in the 30s, where measurements weren't as perfectly standardized as they are now, so I wouldn't be surprised if that was the case.
 
If your 9mm film is too wide to fit in a Minox-type cassette, it's either not 9mm wide or not a Minox-type cassette.

I apologize for my poor English expression skills. What I mean is that the optimal cutting width I've chosen is around 9mm. If I choose a width greater than 9mm, such as 9.2mm, my cassette might not be able to close completely due to some errors or other reasons. If I choose a 9mm cut, even with some errors and other factors, there shouldn't be any major problems.
 
Since I recently summarized everything I know about the dimensions (including thickness) of the original Minox film, this may be of interest in this context: