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Is there a minimum recommended clearance between tyres and seat/chain stays?
Depends what surfaces you're riding on. If you're riding on mud, you need clearance for mud. If you're riding on silky smooth perfect roads, and your wheels are as stiff as hell, you don't need much clearance at all.
5mm is a reasonable starting point though. I'd be a bit wary of having much less, even on a road bike.
Is there a minimum recommended clearance between tyres and seat/chain stays?
Or a rule of thumb as with mudguards, which is 5mm.