Recent advancements in long-read sequencing have enabled the telomere-to-telomere (complete) assembly of a human genome and are now contributing to the haplotype-resolved complete assemblies of multiple human genomes. Since the accuracy of read mapping tools deteriorates in highly-repetitive regions, there is a need to develop accurate, error-exposing (detecting potential assembly errors), and diploid-aware (distinguishing different haplotypes) tools for read mapping in complete assemblies. We describe the first accurate, error-exposing, and partially diploid-aware VerityMap tool for long-read mapping to complete assemblies.