Pixies are definitely authorized, I know a lot of female Sailors who have or have had them.
Navy regulations do not have a minimum length for hair. There's the part about no shaved patches -
Hairstyles shall not be outrageously multicolored or faddish, to include shaved portions of the scalp (other than the neckline), or have designs cut or braided into the hair. - but other than that the only measurements in there are maximums (hair can fall a max of 1 1/2 inches below the jumper collar in whites, bulk of hair can stick out a max of 2" from head for buns) or the size for multiple braids (approx 1/4").
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