Renormalization conjecture for infinitely renormalizable Lorenz-map classes

Fix a topological class $\mathcal{T}$ of infinitely $(a,b)$-renormalizable Lorenz maps, with $a$ and $b$ sufficiently large. Let $\mathcal{U}\subset\mathcal{T}$ be the nonempty open set and let $f^\star\in\mathcal{T}\setminus\mathcal{U}$ be the renormalization fixed point from the coexistence theorem. Let $\mathcal{W}^{\mathrm{u}}$ denote the unstable manifold of $f^\star$, and let rigidity classes and domains of $n$ times renormalizability have their meanings in this setting. Renormalization conjecture for Lorenz-map classes. $\mathcal{T}$ is a codimension-$2$ manifold and $f^\star$ is hyperbolic. For $a$ and $b$ sufficiently large, $\dim\mathcal{W}^{\mathrm{u}}=3$, $\mathcal{T}\setminus\mathcal{U}$ is the stable manifold of $f^\star$, $\mathcal{U}$ is foliated by codimension-$1$ rigidity classes while $\mathcal{T}\setminus\mathcal{U}$ is the rigidity class of $f^\star$, and a generic $2$-dimensional family $\mathcal{F}$ intersects $\mathcal{U}$ in a unique rigidity class. The domains of $n$ times renormalizability inside $\mathcal{F}$ shrink super-exponentially in a universal way; if $\mathcal{F}$ intersects $\mathcal{U}\setminus\mathcal{T}$, then generically these domains shrink exponentially in a universal way. The conjecture describes the expected structure behind coexistence, instability, and parameter universality for these Lorenz-map classes; the source presents the preceding manifold and unstable-manifold results as theorems but leaves this stronger structural statement conjectural.