Two problems in comparative prime number theory: the five-way race modulo 11, and the sign of the integrated prime counting error

We resolve two problems of Hamieh, Kadiri, Martin and Ng in comparative prime number theory. Under GRH and the usual linear-independence hypothesis, we compute all 120 logarithmic densities in the five-way prime number race among the quadratic residues modulo 11, prove that they form eight strictly ordered symmetry classes, and give rigorous enclosures. We also classify the residue-class pairs for which the integrated prime counting error is eventually negative. Both parts use Turing-certified zero lists and rigorous bounds for omitted zeros.