Conjecture that the exact induced density formula holds for all graph sizes

Let $H$ be a strongly asymmetric graph on $h$ vertices. Let $i_H(n)$ be the maximum number of induced copies of $H$ in an $n$-vertex graph, and let $g(n,h)$ be the recursively defined nested-blowup count. Exact density conjecture. For every $n\in\mathbb{N}$,

$$i_H(n)=g(n,h).$$

Consequently, the inducibility of $H$ satisfies

$$i_H=\frac{h!}{h^h-h}.$$

The preceding theorem establishes the formula only in the range covered there; this conjecture proposes its extension to all $n$ for strongly asymmetric graphs.