Stability conjecture for normal bundles of general canonical curves

Let $C$ be a general canonical curve of genus $g\geq 7$, embedded by its canonical linear system in ${\mathbf P}^{g-1}$, and let $N_{C/{\mathbf P}^{g-1}}$ denote its normal bundle. Normal-bundle stability conjecture. The normal bundle

$$N_{C/{\mathbf P}^{g-1}}$$

is stable. The genus-$7$ case is established in the source for curves with maximal Clifford index, while the assertion for general genus $g\geq 7$ remains open. It extends the known stability result in genus $7$ beyond that case.