s-injectivity conjecture for tensor tomography on nontrapping surfaces

Let $(M,g)$ be a compact nontrapping surface with strictly convex boundary. For a smooth symmetric $m$-tensor field $f$ on $M$, let $I_m f$ denote its ray transform. A tensor field is potential if it has the form $dh$ for some smooth symmetric $(m-1)$-tensor field $h$ on $M$ with $h|_{\partial M}=0$. s-injectivity conjecture. If

$$I_m f=0,$$

then $f=dh$ for some such $h$. If $m=0$, then $f=0$. This predicts s-injectivity of the ray transform on all symmetric tensors for compact nontrapping surfaces with strictly convex boundary; the preceding theorem establishes the result under additional assumptions on $I_0$, $I_1$, and $I_0^*$, while the conjecture removes those assumptions.