这篇论文用数学证明加更多验证门不如换不同模型或模态，部分相关会让可靠性提升远不如预期。
本文研究LLM安全带中部分相关验证器级联的可靠性。与条件独立下的对数赔率线性增长（Odds Law, arXiv:2606.15712）不同，部分相关下后验对数赔率对k呈凹性，失败概率多项式衰减（例如Beta(a,b)潜伏下1-r_k ∝ k^{-b}, ρ_v=1/(a+b+1)）。盲点原子（质量1-π）在α=1处限制证据上限为-ln(1-π)纳特。实验显示独立假设在k=5时低估失败20倍，k=10时低估约3000倍，而R=8次重复判决的相关拟合能追踪实际深度。有效杠杆是去相关（更换模型族、模态或证据源），而非增加门数。
Partially Correlated Verifier Cascades in LLM Harnesses: Concave Log-Odds, Polynomial Reliability, and Blind-Spot Ceilings
Serial verification gates are a core reliability primitive in LLM harnesses: a candidate answer is returned only if $k$ verifier calls all accept it. Under conditionally independent gates, the recent Odds Law (arXiv:2606.15712) shows that posterior log-odds grow linearly in $k$, so failure decays exponentially, and states that "a tight theory of partially correlated verifier cascades remains open." This note gives a minimal such theory. Modeling the per-instance false-accept rate on the generator's own errors as a latent variable $α\sim G$ (de Finetti), the exact cascade posterior is $\ell_k = \ell_0 - \ln m_k$, with $m_k$ the $k$-th moment of $G$. Then: (i) $\ell_k$ is concave in $k$ for every non-degenerate $G$ -- the Odds Law is its tangent at the first gate and an upper bound; (ii) for Beta$(a,b)$ latents, failure decays polynomially, $1-r_k \asymp k^{-b}$, with correlation parameter $ρ_v = 1/(a+b+1)$; (iii) a blind-spot atom of mass $1-π$ at $α=1$ caps the evidence extractable from any number of gates at $-\ln(1-π)$ nats, so reliability saturates below 1; (iv) letting the true-accept rate also vary ($β\sim H$) yields a trichotomy -- gates eventually always help, plateau, or actively harm -- decided by the upper-tail exponents of $G$ and $H$, with closed-form crossover $k^\dagger$. The mechanism is survivorship: errors surviving gates are the high-$α$ ones. The theory is measurable: $R$ repeated verdicts per instance identify the first $R$ moments of $G$, so two verdicts identify $ρ_v$; beta-binomial likelihood and NPMLE recover the reliability curve and the ill-posed ceiling. In synthetic tests, independence-based extrapolation underestimates failure by 20x at $k=5$ and ~3000x at $k=10$; the correlated fit at $R=8$ tracks held-out depths. The practical lever is decorrelation -- changing model family, modality, or evidence source -- not adding gates.