Triangle Conjecture

Consider the word-RAM model of computation with word length $O(\log b)$ for inputs of length $b$. An undirected graph $G$ has $m$ edges. Triangle Conjecture. There exists a constant $\epsilon>0$ such that every algorithm in this model that correctly reports whether $G$ contains a triangle has running time $\Omega(m^{1+\epsilon})$. This conjecture is a standard conditional assumption for lower bounds in dynamic graph algorithms; the source gives no resolution of it.