  In the last two decades there have been tremendous attempts to built an
adequate theory of high-temperature superconductivity. Most studies (including
our efforts) used some model Hamiltonians with input parameters not directly
related to the material. The dielectric response function of electrons in
strongly correlated high-temperature superconductors is apriori unknown. Hence
one has to start with the generic Hamiltonian including unscreened Coulomb and
Froehlich electron-phonon interactions operating on the same scale since any
ad-hoc assumption on their range and relative magnitude might fail. Using such
a generic Hamiltonian I have built the analytical theory of high-temperature
superconductivity in doped polar insulators predicting the critical temperature
in excess of a hundred Kelvin without any adjustable parameters. The
many-particle electron system is described by an analytically solvable
polaronic "t-Jp" Hamiltonian with reduced hopping integral, t, allowed double
on-site occupancy, large phonon-induced antiferromagnetic exchange, Jp >> t,
and a high-temperature superconducting state of small superlight bipolarons
protected from clustering.
