# CSM_RH Paper 39 v0.1

Campaign 38 asks whether the arbitrary fixed log-power accuracy of the 2026 Lambda-Lambda-sharp higher-uniformity theorem can be converted to a fixed X-power by taking A=A(X).

Main results:
- fixed power requires A ~ eta log X/log log X;
- the proof uses W=log^(100A) X, which therefore becomes W=X^(100 eta+o(1));
- Lemma 3.5 itself would convert polynomial W into fixed-power Type-II output and a power-small exceptional set;
- the structural W<=X^(epsilon/1000) restriction still leaves a tiny positive eta window;
- the obstruction is the pointwise Dirichlet-polynomial input used to authorize W;
- the prequel Möbius bound, if extended uniformly to growing A, would imply M(X)<<X^(1-eta+o(1)) by partial summation;
- fixed-power Mertens implies a fixed zero-free strip for zeta;
- therefore the current pointwise growing-accuracy route is circular at fixed-power strength;
- fixed-A exceptional-set constants are also not supplied uniformly in growing A;
- Campaign 39 tests whether averaged Dirichlet-polynomial large-value estimates can replace the pointwise input and thereby avoid the Mertens lock.

No proof or disproof of RH is claimed.