Successive intermittency thresholds in dimensions at least four

Let $d$ denote the spatial dimension, and let $\kappa$ be the diffusion constant of the reactant. For $p=2,3,\ldots$, write $p$-intermittent for the corresponding $p$th-order intermittency property.

Threshold conjecture. In $d\geq4$, there exists a strictly increasing sequence $0<\kappa_2<\kappa_3<\ldots$ such that, for $p=2,3,\ldots$, the system is $p$-intermittent if and only if $\kappa\in[0,\kappa_p)$.

This conjecture gives a successive-merging picture for the Lyapunov-exponent curves in dimensions at least four. The paper states that it remains open whether intermittency persists for all large diffusion constants in these dimensions.