UNIFORMIZATION OF SOME WEIGHT 3 VARIATIONS OF HODGE STRUCTURES, ANOSOV REPRESENTATIONS, AND LYAPUNOV EXPONENTS

The paper proves the Lyapunov sum formula and the bad-locus dichotomy under Assumption A using analytic ‘steepness’/gradient-flow estimates (Theorem 2.2.8) and a uniformization of the domain of discontinuity via developing maps (Theorem 2.4.6), then plugs this into the EKMZ framework to conclude the formula (Remark 2.2.10). The candidate solution derives the Lyapunov sum via a Poincaré–Lelong/curvature argument on the reduced wedge W and identifies W^{0,4} ≅ V^{0,3} ⊗ V^{1,2}, and argues the bad-locus dichotomy via local Harish–Chandra normal form plus Schwarz–Pick/Yau. Both approaches are correct and yield the same conclusions, but the techniques are distinct.