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pass-at-k

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The pass@k crossover in RLVR is a theorem, not a finding: pass@k is the Laplace transform of difficulty, so sharpening forces base and RL curves to cross exactly once (Karlin variation-diminishing), with a closed-form pivot and a one-bit certificate for the 'does RL expand reasoning?' debate.

  • Updated Jul 3, 2026
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