The symmetry of rare-earth metals (REM) and f.c.c.-Ce ‘paradox’ are calculated by means of the method of many-electron operator spinors (MEOS). Spin and orbital MEOS factors with [0001] axis of quantization of the angular moment $J$ are responsible for hexagonal deformation $\Delta(c/a) \propto J^{2}$. Indirect covalent $4f—4f$ bond via band fermions adds the bond energy $E_{4f} \propto n_{f}$. Covalent electron collectivization ($n_{f} = 2$) for Ce($4f^{2}$) gives $J \rightarrow 0$ and $\Delta(c/a) = 0$. In the REM-Ce, there is instability of $4f$-shell contributing to the appearance of $5d$-states with amplitude $\xi_{d}(T)$. Covalent bond $\Gamma^{dd}(k)$ (in the MEOS method) appears because of the chemical-bond fluctuations (CBF) for temperature $T > T_{+}$ in the form of $\xi_{d} (T > T_{+})$ jump. Hysteresis of the f.c.c.—f.c.c. $\alpha-\gamma$-transition is caused by the band—covalent bond $\gamma_{b-c}$. Its maximum width $\Delta T_{h} \propto \gamma_{b-c}^{2/3}$ determines jumps of the volume $\Delta \omega(T_{+})$, entropy $\Delta S(T_{+})$, electrical resistance (ER) $\Delta R(T_{+})$, etc. Particularly, the ER jump $\Delta R(T_{+}) \propto \Delta T_{h}$. The experimental data are interpreted by the use of results of calculation.