As far as I know there is no minimum requirement for tyre and arch clearance. How ever some thing to consider is a tyre that is static as in not moving stays flat across it's width, but a tyre that is only running 18-22 psi doing 70mph+ will bulge with centrifugal force making it maybe 10-15mm bigger in the centre. A tyre with low pressure will also have more flex in the side walls, so in short don't make your cycle wings to tight to the tyres.
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