A curved three-dimensional simplex Hilbert transform

We prove Lebesgue space estimates for a curved three-dimensional simplex Hilbert transform associated with the moment curve $t\mapsto (t,t^2,t^3)$. The analysis relies on smoothing inequalities for curved multilinear averages and on estimates for a three-dimensional anisotropic variant of the twisted paraproduct. The result has been formally verified in Lean 4.