Hall and Wellner proposed a natural extension of the Kolmogorov-Smirnov simultaneous confidence band for survival curve using the Kaplan-Meier estimator. They and Gill conjectured that the confidence band holds for all t up to the last observed failure time. A counterexample is given herein, showing that this may not always be true.
"A counterexample to a conjecture concerning the Hall-Wellner band." Ann. Statist. 24 (2) 641 - 646, April 1996. https://doi.org/10.1214/aos/1032894456