inf(M \ L) = 3

The paper proves the explicit lower bound dim_H((M \ L) ∩ (3,3+ε)) ≥ W(e^{c0}|log ε|)/|log ε| − O(log|log ε|/|log ε|^2) (Theorem 1.2) via a concrete construction (local uniqueness + self-replication) and Cantor-set dimension estimates, and from this deduces inf(M\L)=3 and a liminf ≥ 1/2 proportion statement near 3. The candidate solution reproduces the same bound by combining the JEMS asymptotic for d(3+ε) with a “half-share” lower bound, effectively re-packaging the paper’s main theorem rather than reconstructing its proof. Minor issues: the candidate inverts the logical order (treating inf(M\L)=3 as an input instead of a consequence) and treats the 1/2 proportion as a premise rather than as a corollary of the explicit bound and the JEMS asymptotic. Otherwise, conclusions match the paper’s results. See the paper’s equation (1.2) and Theorem 1.2 for the key bounds and their relation to W and c0.