The bounded-chaos conjecture for a rigorous EMCHS outcome

Let $\chi$ be the chaotic map used in the EMCHS model, let $y_0\in[0,1]$, and let $\rho(y)$ denote the proposed invariant density. For a suitable class of functions $g$, bounded-chaos conjecture. The averages

$$\frac{1}{N}\sum_{n\leq N}g(\chi^n(y_0))$$

converge to

$$\int_0^1g(y)\rho(y)\,dy$$

uniformly in $y_0$. Assuming this conjecture together with the Generalized Riemann Hypothesis, an implementation of EMCHS would yield infinitely many prime gaps at most $200$. The proposed result is a speculative route to rigor: neither the stated bounded-chaos input nor the resulting prime-gap conclusion is established in the source.