  Applying Elie Cartan's classical method, we show that the biholomorphic
equivalence problem to a totally nondegenerate Beloshapka's model of CR
dimension one and codimension $k> 1$, whence of real dimension $2+k$, is
reducible to some absolute parallelism, namely to an {e}-structure on a certain
prolonged manifold of real dimension either $3+k$ or $4+k$. The proof relies on
the weight analysis of the structure equations associated with the mentioned
problem of equivalence. Thanks to the achieved results, we prove Beloshapka's
maximum conjecture about the rigidity of his CR models of certain lengths equal
or greater than three: "CR automorphism Lie groups of these models do not
contain any nonlinear map, preserving the origin". Here, we mainly deal with CR
models of the fixed CR dimension one though the results seem generalizable by
means of certain analogous proofs.
