  It was recently conjectured that, in SU(3) gauge theories with fundamental
quarks, valence spontaneous chiral symmetry breaking is equivalent to
condensation of local dynamical chirality and appearance of chiral polarization
scale $\Lambda_{ch}$. Here we consider more general association involving the
low-energy layer of chirally polarized modes which, in addition to its width
($\Lambda_{ch}$), is also characterized by volume density of participating
modes ($\Omega$) and the volume density of total chirality ($\Omega_{ch}$). Few
possible forms of the correspondence are discussed, paying particular attention
to singular cases where $\Omega$ emerges as the most versatile characteristic.
The notion of finite-volume "order parameter", capturing the nature of these
connections, is proposed. We study the effects of temperature (in N$_f$=0 QCD)
and light quarks (in N$_f$=12), both in the regime of possible symmetry
restoration, and find agreement with these ideas. In N$_f$=0 QCD, results from
several volumes indicate that, at the lattice cutoff studied, the deconfinement
temperature $T_c$ is strictly smaller than the overlap-valence chiral
transition temperature $T_{ch}$ in real Polyakov line vacuum. Somewhat similar
intermediate phase (in quark mass) is also seen in N$_f$=12. It is suggested
that deconfinement in N$_f$=0 is related to indefinite convexity of absolute
X-distributions.
