The universal upper-bound conjecture for proportional cake-cutting with different entitlements

Let $n$ be a positive integer, let there be $n$ value measures on a cake, and let $t$ be an entitlement vector. A $t$-proportional allocation assigns each agent a piece whose value according to that agent's measure is at least their entitlement.

Universal upper-bound conjecture. For every $n$, every set of $n$ value measures, and every entitlement vector $t$, there exists a $t$-proportional allocation with at most $2n-2$ cuts.

The preceding theorem establishes this bound when at least $n-1$ entitlements are equal to $1/D$ for some integer $D\geq 1$. The conjecture asserts that the same lower bound is always attainable; the simplest case in which it remains open is $n=3$ with entitlements $(1/7,2/7,4/7)$.