# CSM_RH Paper 38 v0.1

Campaign 37 tests whether the Gafni-Tao exceptional-set proof can be upgraded from fixed relative threshold to a polynomially shrinking threshold.

Main results:
- the published theorem fixes delta and J before X tends to infinity;
- a threshold delta forces explicit-formula height T >= delta^{-1} X^(1-theta) log^2 X;
- delta=X^(-eta) therefore adds +eta to the zero-density height exponent;
- the decisive right-edge lemma has only stretched-log suppression, exp(-c (log X)^(1/3)/(log log X)^(1/3));
- this is much larger than X^(-eta) for every fixed eta>0;
- standard L2, L4, and hypothetical 2k-th moment Markov arguments cannot repair the shrinking edge because the threshold penalty survives as sigma tends to 1;
- the interior Guth-Maynard density region can retain exponent room for small eta if a fixed right-edge gap were hypothetically supplied;
- no shrinking-threshold theorem is proved;
- Campaign 38 moves to the independent 2026 Lambda-Lambda-sharp higher-uniformity route and audits growing accuracy A=A(X).

No proof or disproof of RH is claimed.