  We introduce a minimal model for 2D cuprates with the on-site Hilbert space
reduced to only three effective valence centers CuO$_4^{7-,6-,5-}$ (nominally
Cu$^{1+,2+,3+}$) and make use of the S=1 pseudospin formalism. Despite its
seeming simplicity the model is believed to capture the salient features both
of the hole- and electron-doped cuprates. The pseudospin formalism elucidates
an unique fermion-boson duality of the doped cuprates, does provide an unified
standpoint for classification of the "myriad"\, of electronic phases in
cuprates and the evolution of the CuO$_2$ planes under a nonisovalent doping,
introduces the on-site mixed valence quantum superpositions and order
parameters to be novel features of the cuprate physics, does provide a
comprehensive description of the correlated one- and two-particle transport,
coexistence of $p$- and $n$-type carriers, electron-hole asymmetry,
anticorrelation of conventional spin and superconducting order parameters.
Concept of the electron and hole centers, differing by a composite local boson,
and electron-hole pairing are shown to explain central points of the cuprate
puzzles, in particular, the HTSC itself, pseudogap, and Fermi surface
reconstruction.
