Entropy of Lyapunov Maximizing Measures of GL(2,R) Typical Cocycles

The paper’s main claim (Theorem 1.2) matches the candidate solution’s conclusion: under 1-pinching, 1-twisting, and the NOC on the Mather set K, every Lyapunov maximizing measure has zero entropy . However, the paper reduces to a subshift setting and then asserts that Bochi–Rams’ argument extends, providing only partial details and stating that “the rest of the proof … will work … up to some minor modifications,” which is insufficient as written . By contrast, the candidate solution gives a coherent cone-contraction/Hilbert-metric proof sketch that directly yields zero entropy from forward cone invariance plus forward NOC, with pinching/twisting used only earlier to guarantee domination/NOC on K, consistent with the paper’s setup (domination ⇔ invariant multicone; definition of NOC) .