So this is a question about which way the growth rings should appear on the end of a board. Case in point: I’m in the middle of replacing an oak threshold for my home’s side door. The original (1910) is almost two inches thick by 8″ x 40″ and it’s cup “up”. It wasn’t split but rather weather beaten. I know most furniture makers alternate boards when making a table top but this will be just one thick board and it was pricy. I’d like to give it its best chance for another long life.
Best regards
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Wood cups in the opposite direction of the rings - so if the end of the board is smiling, the board will frown. I would recommend putting the rings' "smile up" for the threshold so that if any cupping occurs over time, the edges stay down to the floor and the center rises.
However, if installed in construction adhesive and fastened adequately it should stay flat enough.
Also, for what it's worth, the "alternating rings" theory is more of an old wives' tale than backed by science when the moisture content is controlled and the wood is properly dried to start. If you're so inclined, plenty of fun reading of lively conversations on the topic over at wood-web: https://www.woodweb.com/knowledge_base/Alternating_growth_rings_in_panels.html