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Given a pseudo-effective divisor $L$ we construct the diminished ideal ${𝒥}_{\sigma }\left(L\right)$, a “continuous” extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. Our main theorem shows that for most pseudo-effective divisors $L$ the multiplier ideal $𝒥\left(h_{\min }\right)$ of the metric of minimal singularities on ${𝒪}_X\left(L\right)$ is contained in ${𝒥}_{\sigma }\left(L\right)$. We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.