We report on the first multi-differential measurement of $phi$ meson and $Xi^{-}$ hyperon production as well as the $phi/K^-$ and $phi/Xi^-$ ratio in Au+Au collisions at ${sqrt{s_{rm NN}} = rm{3,GeV}}$ with the STAR experiment under its fixed targ et configuration at RHIC. $phi$ mesons and $Xi^{-}$ hyperons are measured through their hadronic decay channels, $phirightarrow K^+K^-$ and $Xi^-rightarrow Lambdapi^-$. The transverse kinetic energy spectra of $K^-$, $phi$ and $Xi^{-}$ are presented in different centrality and rapidity intervals. The total production yields and the ratios within a $4pi$ coverage are calculated and compared to thermal model predictions. A calculation within the grand canonical ensemble framework shows a clear discrepancy from our measurement. Our data favor the canonical ensemble approach employing local strangeness conservation with a small strangeness correlation length ($r_c leq 4.2$ fm) in 0--10% central Au+Au collisions at ${sqrt{s_{rm NN}} = rm{3,GeV}}$.
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