  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-group
invariant quantities in these correlations are the ratio of the strange to
non-strange quark mass $r_m=m_s/m_q$, the condensate ratio $r_c=\langle \bar s
s\rangle/\langle \bar q q\rangle$, 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 define
a self-consistent trajectory in the $\{r_m,r_c,r_p\}$ parameter space
constraining strange quark parameters that can be used to assess the
compatibility of different predictions of these parameters. Combining the
constraint with Particle Data Group (PDG) values of $r_m$ results in
$\{r_c,r_p\}$ constraint trajectories that are used to asses the
self-consistency of various theoretical determinations of $\{r_c,r_p\}$. The
most precise determinations of $r_c$ and $r_p$ are shown to be mutually
consistent 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 direct
determinations. The $\{r_c,r_p\}$ correlations provide a natural identification
of a self-consistent set of strange quark mass and strange quark condensate
parameters.
