Hudson's conjecture on trivial source Specht modules of 2-weight 2

Let $\mathfrak{S}_n$ be the symmetric group, let $\mathbb{F}$ be an algebraically closed field of characteristic $p$, and let $S^\lambda$ denote the Specht module labelled by a partition $\lambda$ of $n$. A partition has 2-weight $2$ when its $2$-weight is $2$, and a trivial source Specht module is a Specht module that is a trivial source module. Hudson's conjecture. Let $p=2$. Then every trivial source Specht module labelled by a partition with $2$-weight $2$ is either simple or isomorphic to a Young module. The paper studies the classification of trivial source Specht modules and proves this assertion for partitions with $2$-weight $2$, so the conjecture is resolved.