Chekanov's augmentation-independence conjecture for first-order Poincaré–Chekanov polynomials

Let $(A,\partial)$ be the differential graded algebra of a Legendrian knot, let $\varepsilon$ be an augmentation of $A$, and let the first-order Poincaré–Chekanov polynomial be the polynomial associated to this augmentation. Chekanov's augmentation-independence conjecture. The first-order Poincaré–Chekanov polynomial is independent of the augmentation $\varepsilon$. The source attributes this conjecture to Chekanov. It is related to the tangent-space interpretation of the polynomial in the associated scheme, but the supplied text gives no resolution.