Genericity results for singular curves

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Geometric Approach to Pontryagin’s Maximum Principle (2008, background): “That is why the existence or non–existence of abnormal minimizers is only known for specific control problems, mainly control–linear and control–affine systems with control–quadratic cost functions or for time–optimal control problems [4, 6, 19, 26, 27, 77].”
On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures (2018, unknown): “It is known that a generic sub-Riemannian structure of rank larger than 2 does not have non-constant abnormal extremals satisfying the Goh condition [CJT06].”
Invariant Carnot-Caratheodory metrics on $S^3$, $SO(3)$, $SL(2)$ and lens spaces (2007, unknown): “For a deep analysis of abnormal extremals in sub-Riemannian geometry, see [8, 15].”
Small time heat kernel asymptotics at the sub-Riemannian cut locus (2012, background): “For a discussion of the presence of strictly abnormal minimizers in sub-Riemannian geometry one can see [27].”
A Comprehensive Introduction to Sub-Riemannian Geometry (2019, background): “When the rank of the distribution is larger or equal than 3, Goh conditions are not satisfied for generic distributions as proved in [CJT06].”