Uniform computation of the squared-logarithmic k-server bound

We construct a uniform randomized k-server algorithm on finite rational metrics with competitive ratio $O({\log }^2(k+1))$ against oblivious request sequences. Preprocessing is polynomial in the input length, and per-request bit complexity is polynomial in that length and the binary request-counter length. The additive movement constant is finite and instance-dependent, but may be enormous. The construction uses the companion squared-logarithmic existence theorem.