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Correlations between the strange quark mass, strange quark condensate$\langle \bar s s\rangle$, and the kaon partially conserved axial current(PCAC) relation are developed. The key dimensionless and renormalization-groupinvariant quantities in these correlations are the ratio of the strange tonon-strange quark mass $r_m=m_s/m_q$, the condensate ratio $r_c=\langle \bar ss\rangle/\langle \bar q q\rangle$, and the kaon PCAC deviation parameter$r_p=-m_s\langle \bar s s+\bar q q\rangle/2f_K^2m_K^2$. The correlations definea self-consistent trajectory in the $\{r_m,r_c,r_p\}$ parameter spaceconstraining strange quark parameters that can be used to assess thecompatibility of different predictions of these parameters. Combining theconstraint with Particle Data Group (PDG) values of $r_m$ results in$\{r_c,r_p\}$ constraint trajectories that are used to asses theself-consistency of various theoretical determinations of $\{r_c,r_p\}$. Themost precise determinations of $r_c$ and $r_p$ are shown to be mutuallyconsistent with the constraint trajectories and provide improved bounds on$r_p$. In general, the constraint trajectories combined with $r_c$determinations tend to provide more accurate bounds on $r_p$ than directdeterminations. The $\{r_c,r_p\}$ correlations provide a natural identificationof a self-consistent set of strange quark mass and strange quark condensateparameters.

Correlations between the strange quark condensate, strange quark mass, and kaon PCAC relation