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We construct canonical absolute parallelisms over real-analytic manifoldsequipped with $2$-nondegenerate, hypersurface-type CR structures of arbitraryodd dimension not less than $7$ whose Levi kernel has constant rank belongingto a broad subclass of CR structures that we label as recoverable. For this wedevelop a new approach based on a reduction to a special flag structure, calledthe dynamical Legendrian contact structure, on the leaf space of the CRstructure's associated Levi foliation. This extends the results ofPorter-Zelenko [20] from the case of regular CR symbols constituting a discreteset in the set of all CR symbols to the case of the arbitrary CR symbols forwhich the original CR structure can be uniquely recovered from itscorresponding dynamical Legendrian contact structure. Our method clarifies therelationship between the bigraded Tanaka prolongation of regular symbolsdeveloped in Porter-Zelenko [20] and their usual Tanaka prolongation, providinga geometric interpretation of conditions under which they are equal. Motivatedby the search for homogeneous models with given nonregular symbol, we alsodescribe a process of reduction from the original natural frame bundle, whichis inevitable for structures with nonregular CR symbols. We demonstrate thisreduction procedure for examples whose underlying manifolds have dimension $7$and $9$. We show that, for any fixed rank $r>1$, in the set of all CR symbolsassociated with 2-nondegenerate, hypersurface-type CR manifolds of odddimension greater than $4r+1$ with rank $r$ Levi kernel, the CR symbols notassociated with any homogeneous model are generic, and, for $r=1$, the sameresult holds if the CR structure is pseudoconvex.

On geometry of $2$-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations