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Applying Elie Cartan's classical method, we show that the biholomorphicequivalence problem to a totally nondegenerate Beloshapka's model of CRdimension one and codimension $k> 1$, whence of real dimension $2+k$, isreducible to some absolute parallelism, namely to an {e}-structure on a certainprolonged manifold of real dimension either $3+k$ or $4+k$. The proof relies onthe weight analysis of the structure equations associated with the mentionedproblem of equivalence. Thanks to the achieved results, we prove Beloshapka'smaximum conjecture about the rigidity of his CR models of certain lengths equalor greater than three: "CR automorphism Lie groups of these models do notcontain any nonlinear map, preserving the origin". Here, we mainly deal with CRmodels of the fixed CR dimension one though the results seem generalizable bymeans of certain analogous proofs.

Biholomorphic equivalence to totally nondegenerate model CR manifolds and Beloshapka's maximum conjecture