Every Weak Perron Number is an End-Periodic Stretch Factor

Given any weak Perron number $\lambda$, we construct an end-periodic homeomorphism $f:\mathrm{\Sigma }\to \mathrm{\Sigma }$ with Handel-Miller stretch factor equal to $\lambda$ where $\mathrm{\Sigma }$ is a connected infinite-type surface with finitely many ends all accumulated by genus.