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Default frame and panel chest - question minimum rail size

In process of making a cherry frame and panel blanket chest, 40" long x
19" high x 18" deep (approx.) Corner legs (stiles) are 1-3/4" square
(finished dimension); question is, for this length, how narrow can I
make the top and bottom rails? I plan on using 3/4" finished dimension
stock for the rails, and there would be a single panel, probably solid
wood, grain running horizontally, of approx. 38" x 12" or so; it would
sit in a 1/4" or 3/8" groove in rails/stiles. And, stiles would be
mortised to fit a 3/4" long tenon in rails. Suggestions appreciated.