4 problems

The modular-lattice integrality conjecture. Every modular lattice is integral.

Let $P$ be an upho modular lattice, meaning that $P$ is of finite type and its principal order filter at every element is isomorphic to $P$. Suppose that $P$ is indecomposable and…

Let $\mathcal{X}$ be a lattice with lattice operations $\land$ and $\lor$. Suppose that the inequality … holds for all $x,a,y,b,z\in\mathcal{X}$, where $L$ and $U$ are the five-var…

Hernandez–Sethuraman conjecture. The secrecy function conjecture should be true when the normalization is done using $D^{\ell}$ instead of the scaled cubic lattice. The supplied te…