Prolate quadrature error conjecture for lower-index prolate functions

Let $c>0$ be a positive real number and let $n>2c/\pi$ be an integer. Let $0\leq m<n$ be an integer. Let $t_1,\dots,t_n$ and $W_1,\dots,W_n$ be the nodes and weights of the quadrature introduced in the source. Let $\psi_m$ be the corresponding prolate function and let $\lambda_n$ be the associated eigenvalue.

Quadrature-error conjecture. The quadrature error satisfies

$$\left|\int_{-1}^1\psi_m(s)\,ds-\sum_{j=1}^n\psi_m(t_j)W_j\right|\leq|\lambda_n|.$$

The conjecture is motivated by numerical tables showing that the absolute error is bounded by, and is roughly half of, $|\lambda_n|$, whereas the previously proved upper bound is more cautious. Its resolution is not given in the supplied text.