Does $\max_{n<x}d_n d_{n-1}\big/(\max_{n<x}d_n)^2\to 0$ for prime gaps $d_n$? (Erdős #1137)

Let $d_n=p_{n+1}-p_n$ be the $n$th prime gap. Vaughan asked whether $$\frac{\max_{n<x} d_n\,d_{n-1}}{\big(\max_{n<x} d_n\big)^2}\longrightarrow 0\quad\text{as }x\to\infty.$$ Intuitively: the largest PRODUCT of two consecutive gaps below $x$ should be asymptotically negligible compared with the square of the single largest gap — i.e. record gaps do not come in adjacent pairs of comparable size. Both the numerator and denominator are exact finite maxima over a prime table, so the ratio $R(x)$ is directly computable. GOAL (computational): compute $R(x)$ at many increasing values of $x$ (tracking the record gaps and record adjacent-gap products), and report whether $R(x)$ is decreasing toward $0$.

Acceptance. PARTIAL / PRIMARY (finite, machine-checkable): the ratio $R(x)=\max_{n<x}(d_n d_{n-1})/(\max_{n<x}d_n)^2$ evaluated at a growing sequence of $x$ (state the maximum $x$; leverage published tables of maximal prime gaps, e.g. up to $x\sim 10^{18}$, or a direct sieve to a feasible bound), delivered with (i) a runnable script and (ii) a table/plot of $R(x)$ vs $x$ together with the record gap and record adjacent-gap-product witnesses. A clearly decreasing $R(x)$ is evidence for the conjecture. FULLY RESOLVES: a proof that $R(x)\to0$ (or that it does not). State the range of $x$ and the data source (sieve or maximal-gap tables).