Lean 4 checks the complete packed-memory and fresh-random indexed models, hard distribution, communication bounds, separator, nested-forest accounting, deterministic and Las Vegas lower bounds, strict-predecessor reduction, and redundancy corollaries.
A deterministic O(1)-competitive algorithm that allocates k replica GPUs among m experts as workloads change and is machine-checked in Lean 4 relative to the positive-body result as the sole scientific source premise.
A fully online model for batching nonpreemptive LLM requests under a growing KV-cache memory constraint and it is proved that every deterministic algorithm has competitive ratio Omega(sqrt(n), while the elementary sequential upper bound is n.
It is proved that the randomized primal competitive ratio is in fact Theta(1) for arbitrary numbers of experts and the upper bound reduces reciprocal-max service costs to chasing positive bodies with covering row sparsity two.
Ian D'Ambrosio· 0 citations
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