The Maslov-index formula for immersed Lagrangian cylinders

Let $C$ be an immersed Lagrangian cylinder between smoothly concordant Legendrian knots $K_1$ and $K_2$, constructed as in the immersion construction discussed in the paper. Let $\{x_i,y_i\}$, for $i\in\{1,\ldots,k\}$, be cancelable pairs of double points, and let $u_i\in\pi_2(x_i,y_i)$ be Whitney disks for these pairs. Maslov-index conjecture. The Maslov indices satisfy

$$\sum_{i=1}^k\bigl(\mu(x_i,y_i,u_i)-1\bigr)=tb(K_1)-tb(K_2).$$

The conjecture is intended to relate the Maslov indices of cancelable double-point pairs to the Thurston–Bennequin-number difference; the paper notes that an embedded Lagrangian cylinder perturbed to have two transverse double points gives Maslov index $1$ for the pair, but does not establish the general formula.