Research proof index

An unbalancing lemma in physical space. Suppose $\nu$ is a probability weight, $f$ is real-valued, and $f$ and $\nu$ admit self-difference-convolution factorizations $f=g\mathbin{\circleddash}g$ and $\nu=h\mathbin{\circleddash}h$. If $0<\varepsilon\le1$, $p\ne0$, and $\|f\|_{L^p(\nu)}\ge\varepsilon$, then some integer $p'$ satisfies $p'\le 2^{10}\varepsilon^{-2}p$ and $\|1+f\|_{L^{p'}(\nu)}\ge1+\varepsilon/2$.

In a FreeStateTheory, we have free states of full rank, therefore the minimum relative entropy of any state ρ to a free state is finite.

The lemma that the proposition EnergyMass is dimensionally correct

A polynomial is separable if and only if its discriminant is non-zero.

Under per-family upper bounds on the two U-transform oracle families, decapsulation incurs weighted query cost at most the sum of those bounds.

Under per-family upper bounds on the two U-transform oracle families, encapsulation incurs weighted query cost at most the sum of those bounds.