Abundance of strange attractors in the EBM family

Let $\Lambda_t$ be the parameterized EBM map, and let $t_n$ be the sequence appearing in the renormalization conjecture. For each natural number $n$, there exists an interval $I_n$ contained in $(1/\sqrt{2},t_n)$ such that $\Lambda_t$ displays at least $2^{n-1}$ different strange attractors for parameters $t\in I_n$.

Strange-attractor abundance conjecture. For each natural number $n$ there exists an interval $I_n\subset (1/\sqrt{2},t_n)$ such that $\Lambda_t$ displays, at least, $2^{n-1}$ different strange attractors.

The claim predicts arbitrarily large finite multiplicity of strange attractors along the renormalization parameter intervals. The surrounding text states that these conjectures were formulated in earlier work and are proved in the present paper, so the database status is solved.