Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 110-02. Uniform computation of the squared-logarithmic k-server bound
Manuscript map · lines 4625–4634
OpenAI@2026-10-07#rem:oai-p-110-02
Authors: OpenAI. Family 110.
Title: Uniform computation of the squared-logarithmic k-server bound.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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