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As you pull the DH you also SHEET IN that flattens the sail.

yes, but mainly in the top, because the lower part of the mast is still stiffend by the diamonds, if rotated out.
Here is a link to Landenberger sails: trim guide , which fits well to my mast. When I remember back on the Tiger, we used the rotation only between up and down wind, but not with different downhaul setting. Not clear if it because of the jib or the mast profile or because I sail better now (at least I think that I do).

Cheers,

Klaus