Boolean Matrix Multiplication conjecture for combinatorial triangle detection

The Triangle Detection problem asks whether an $n$-node graph contains a triangle. A strongly subcubic combinatorial algorithm is a combinatorial algorithm whose running time is $O(n^{3-\varepsilon})$ for some constant $\varepsilon>0$. Boolean Matrix Multiplication conjecture. There is no strongly subcubic combinatorial Triangle Detection algorithm, equivalently no such algorithm for Boolean Matrix Multiplication, in general $n$-node graphs. This conjecture is a central fine-grained hardness assumption: the best known combinatorial methods for triangle detection are only mildly subcubic, and a strongly subcubic combinatorial algorithm would refute the conjecture. The parser marks this conjecture as disproved, based on the stated reduction relating the general-graph barrier to the BMM conjecture.