NON-STATIONARY VERSION OF FURSTENBERG THEOREM ON RANDOM MATRIX PRODUCTS

The paper proves the expected exponential growth L_n >= nλ via a clean Furstenberg-entropy argument with an additive, per-step positive lower bound h that follows uniformly from the measures condition and compactness (Cor. 2.7, Prop. 2.10), then transfers to matrices using N(f_A)=||A||^d (Prop. 2.1). The candidate solution mis-cites a non-existent Theorem 1.6 and invokes the atoms-dissolving machinery to claim a uniform per-step lower bound on the expected negative log-Jacobian; this key step is not established in the paper and does not follow from Theorem 1.13 (atoms dissolving) or Proposition 1.14 (subspaces avoidance). Hence the model’s proof is unsupported at its core step, even though its final conclusion matches the paper.