Cornwell–Ng–Sivek conjecture on a non-decomposable satellite Lagrangian concordance

Let $\Lambda_{-}$ and $\Lambda_{+}$ be the Legendrian knots described in the satellite construction, and let $P\subset J^1S^1$ be the Legendrian clasp tangle used to form their satellites. The satellite construction produces a Lagrangian concordance from $S(\Lambda_{-},P)$ to $S(\Lambda_{+},P)$. Cornwell–Ng–Sivek's conjecture. The Lagrangian concordance from $S(\Lambda_{-},P)$ to $S(\Lambda_{+},P)$ built through the satellite construction is not decomposable. This conjecture gives a negative answer to the motivating question of whether every connected Lagrangian cobordism admits a decomposable representative; it is attributed to Cornwell, Ng, and Sivek and remains unresolved in the supplied source.