The interpretable-fields conjecture for logarithmic-exponential transseries

Let $\mathbb T$ be the differential field of logarithmic-exponential transseries, and let $\mathbb R$ be the real field. Write $\mathbb T[\imag]$ and $\mathbb C=\mathbb R[\imag]$ for their respective algebraic closures. Interpretable-fields conjecture. The only infinite fields interpretable in $\mathbb T$ are $\mathbb T$, $\mathbb R$, and their respective algebraic closures $\mathbb T[\imag]$ and $\mathbb C=\mathbb R[\imag]$. This is posed as a further expectation after establishing distality of the relevant transseries theories; the source gives no resolution.