Applicability of $a$-Contraction to Artificial Genuinely Nonlinear Systems

Determine whether the artificially constructed genuinely nonlinear hyperbolic systems that admit rank-one connections and non-degenerate $T_4$ configurations are amenable to the $a$-contraction-with-shifts method.

Background

The paper discusses purported constructions of genuinely nonlinear hyperbolic systems possessing rank-one connections and non-degenerate T4T_4 configurations. These systems are highly artificial, nonphysical, and genuinely nonlinear only on a very narrow region.

Because the paper’s stability theory depends on aa-contraction, it identifies as unresolved whether these exceptional geometric constructions also satisfy the structural requirements needed for that method.

References

It is also not clear if these very artificial systems are amenable to $a$-contraction.

— The computational ansatz for convex integration of hyperbolic systems and a resolution of the Strong Trace Conjecture  (2609.09353 - Krupa, 8 Sep 2026) in Section 1, subsection “Further questions on rank-one geometry”