Normal complex surface singularities with rational homology disk smoothings

We prove that a normal surface singularity whose minimal good resolution graph has at least two nodes does not admit a rational homology disk smoothing. Together with the earlier graph classifications and the analytic classifications of Fowler and Wahl, this gives a complete classification of normal surface singularities admitting rational homology disk smoothings and proves Wahl’s conjecture. The same argument also proves Wahl’s Rational Conjecture.