The exact Lagrangian cobordism generation conjecture for Legendrian knots

Let $cLambda$ be a Legendrian knot in $cmathbb{R}^{3}$, and let $L_{cLambda}$ be an exact Lagrangian filling with $cemptysetcprec^{ex}_{L_{cLambda}}cLambda$. The notation $cemptysetcprec^{ex}_{L_{cLambda}}cLambda$ means that $L_{cLambda}$ is an exact Lagrangian cobordism from the empty Legendrian to $cLambda$. Exact Lagrangian cobordism generation conjecture. If $cemptysetcprec^{ex}_{L_{cLambda}}cLambda$, then $L_{cLambda}$ is obtained by stacking exact Lagrangian cobordisms described in the theorem realizing Legendrian isotopy, $0$-resolution at a contractible crossing in the Lagrangian projection, and capping off a $tb=-1$ unknot with a disk. This is a proposed generation statement for exact Lagrangian fillings by the listed elementary cobordisms; the supplied text does not give evidence that it has been proved or disproved.