Wow, she's got a limber back!

The position your daughter is doing is not really a haircutter; it is more difficult than a haircutter because she is leaned way back and holding her blade with both hands. I think it would be classified as a pearl, even though her free leg is less extended than Caroline Zhang's famous pearl position. As long as she can hold that position for 3 revolutions before pulling up to the Biellmann (technically, 2, but 3 is safer if you want them to count it as a separate position), she should be able to get another level for that. I have no doubt that her pearl would qualify as a difficult variation of a layback position based on the definition given by the ISU:
"A difficult variation is a movement of a body part, leg, arm, hand or head,
which requires more physical strength or flexibility and that has an effect on the balance of the main body core."
And once again, it's not all about the levels. You are comparing her layback spin to a level 4 sitspin (8 revs, pancake, etc) but a level 4 sitspin is not worth as many points as a level 4 layback! A LSp4 is worth 2.7 base points and a SSp4 is only worth 2.5. Your daughter can get a level 4 on her layback if she does 8 revs in layback, 3 revs side leaning, 3 revs pearl, then 3 revs Biellmann.
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