[UK] Court of appeal says it cannot rule on which identical twin fathered a child

Both are needed. They are identical twins and you’d need to know which brother has a specific spontaneous mutation or if it was unique to the child.

No, not really. The two brothers are going to have nearly identical alleles. There will be ~100 mutations that are unique to each (de novo germline variants), and maybe hundreds of thousands that they share (inherited germline variants). The child will share ~50% of the father's variants. Identifying the father will involve identifying the 100 unique variants that each brother has, and seeing which of those was inherited by the child. The child should have roughly 50 of the father's unique variants, and zero of the not-fathers. If you only sequence one brother, then you won't know which of the 100,000s of variants are the 100 unique ones to each. Basically, both brothers are very nearly as genetically similar to the child. You need to figure out which brother is *more* similar, which you can't do without knowing exactly how similar each brother is. This is different to a regular paternity test in which you are checking to see if the child is more similar to the potential father than by random chance. You could hypothetically get lucky with one brother, though. If you sequence the false father only, it is possible that some of their unique variants are very close to their non-unique variants. Variants that are very close together on the same chromosome are very likely to be inherited together by the child. (But equally likely to be not-inherited together.) If the child only has one of two very linked variants, it is highly unlikely that the sequenced twin is the father, since statistically, the child should have both or neither, but not just one. But the whole setup of this would be unlikely and difficult.

I can't imagine that would hold up legally. Feels like you'd have to prove that perso specifically,, not rule out the other pitentials till there's one remaining.

I don't think medical-grade WGS will be good enough to identify the rare unique variants that differentiate the twins. Medical things usually rely on a priori knowledge that variants of interest exist. If you are suspected of having a genetic disease, you can get away with poor quality/low depth sequencing if you already know what you're looking for. Semi-crappy evidence of a smoking gun in a pile of debris is pretty good when you know what a gun looks like and you know that there shouldn't be one in the pile in the first place. Trying to find evidence of something when you don't know what you're looking for and there is c*** all over the place is much much harder.

That article doesn’t say anything about the scan itself. The read length and depth make a huge difference, especially if you’re trying to compare what should be identical DNA.

There's also just she and twin B cheated (her and one twin together against the other, and only one twin was tricked)

That seems like a great summary.