Uniform popularity vector uniquely minimizes LRU hit rate H_C(p) on the interior simplex, with strict radial increase proven via explicit positive pair-square formula for the derivative.
Hildebrand, On a conjecture of Fill and Holst involving the move-to-front rule and cache faults,Probability in the Engineering and Informational Sciences13(1999), no
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Radial Extremality for LRU Caching and the Fill--Holst Conjecture
Uniform popularity vector uniquely minimizes LRU hit rate H_C(p) on the interior simplex, with strict radial increase proven via explicit positive pair-square formula for the derivative.