ℓ-layered reachability oracle conjecture

Let $\ell$ be an integer, and let $G$ be an $\ell$-layered directed acyclic graph with layers $L_1,\ldots,L_\ell$, where every edge goes from $L_i$ to $L_{i+1}$. An $\ell$-layered reachability oracle is a data structure for answering whether a vertex in $L_1$ reaches a vertex in $L_\ell$; let $m$ denote the number of edges. Consider the word-RAM model with word length $O(\log b)$ for inputs of length $b$. $\ell$-layered reachability oracle conjecture. There exists a constant $\epsilon>0$ such that every such oracle has preprocessing time $\Omega(m^{1+\epsilon})$ or query time $\Omega(m^\epsilon)$. This conjecture underlies conditional lower bounds for dynamic graph problems. The source attributes it to Alman et al. and gives no resolution; it also notes that the 3LRO conjecture follows from the Triangle and 3SUM conjectures.