No. Check with the tire manufacturer for the specs. Though most new tires are made with tread wear indicators. The ridge in the groove gets even with the tread, time for new tires. You can see them in the pic you posted.
This is a fitness for purpose question. If they are being used as dry condition only and they aren't too old then run 'em as far down as you can stand. This why many "summer spec' high performance tires can be ordered shaved down form Tire Rack etc. All those grooves and blocks are for all/season-wet weather.
Drag Week 2006 & 2012 - Winner Street Race Big Block Naturally Aspirated - R/U 2007 Broke DW '05 and Drag Weekend '15 Coincidence?
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