Holonomy Asymptotics along Quartic Differential Rays

What the math gives to ML

The paper develops a concrete WKB/Stokes factorization for holonomy: propagation along a ray is dominated by exponential phase integrals of four local fourth roots, while crossings of Stokes sectors contribute sparse unipotent matrices. The transferable asset is not the quartic geometry itself but the separation between diagonal growth/decay and determinant-one sparse mode mixing, together with explicit triangular jump factors. This suggests an invertible neural mixing block for sequence or graph representations whose long-range propagation is handled by cheap diagonal phase updates and whose mode conversions are handled by sparse unipotent residual maps. A first test should compare this block with dense linear mixing at matched parameters and FLOPs, measuring stability, reversibility, and optimization speed.