Open. The site labels the problem OPEN (page last edited 28 September 2025). Pollack and Pomerance [PoPo16] proved $h(x)>x^{1.4}$ for all large $x$, which gives $h(x)/x\to\infty$; Erdős [Er74b, p. 202] had sketched only $\limsup h(x)/x=\infty$, writing that the proof of $h(x)/x\to\infty$ "can be produced with a little more trouble". A partial result is claimed on the site's proof-claims tab (claim by Cam, using GPT 5.6 high, submitted 2026-08-28): the write-up claims $h(x)>x^{\gamma}$ for every fixed $\gamma<13/8$ and all large $x$, with squarefree pairs, by the scheme of [PoPo16] with Pascadi's level $5/8$ of distribution for primes in place of Baker and Harman's count of smooth shifted primes. A bound below exponent $2$ settles no instance of the question, so the claim has no claim page; the proof-claims thread had no comments as of 2026-10-06.