A Deterministic Constant-Competitive Algorithm for Dynamic Mixture-of-Experts Serving

Version 3 strengthens the Dynamic Mixture-of-Experts Serving result from a randomized constant-competitive integral algorithm to a deterministic one. The new pathwise rounding theorem has service distortion three and movement at most the fractional internal variation plus 6k. Composing it with the positive-body reduction gives ALG_det <= 10 C_PB OPT + (5 C_PB + 8) k + 16, and therefore CR_det(k)=Theta(1). The accompanying archive contains the complete positive-body reduction, deterministic Lean 4 proof, exact rational controls, pinned-source bootstrap, canonical evidence files, merged manuscript source, rendered PDF, and one-command verifier. Beyond, the research system operated by Nth Research Collective, materially assisted with literature retrieval, hypothesis generation, formalization, executable controls, and adversarial review. The author made the final scientific judgments and accepts full responsibility for the work.