# CSM_RH Paper 42 v0.1

Campaign 41 attacks the pure-Möbius Type-II core in its translated high-frequency window.

Main results:
- exact Gaussian-smoothed translated mean-square identity for the pure-core Dirichlet polynomial;
- the diagonal is only Y/X times polylog and is far below the polynomial-W target in the current Type-II range;
- Gaussian smoothing rapidly removes far shifts;
- the ultra-short shell h<=X/Q is harmless by absolute values because the large major-arc center Q is polynomially larger than the local window Y;
- the only hard shell is X/Q < h <= X^(o(1)) X/Y;
- this shell is an oscillatory shifted correlation of the balanced restricted Möbius-convolution coefficient c_X;
- current averaged Chowla technology gives qualitative/logarithmic rather than fixed X-power cancellation and does not directly cover c_X;
- standard zero detection uses a composite polynomial and does not provide a certified theorem that one individual short dyadic Möbius block must resonate at an off-line zero ordinate;
- therefore the high-frequency route remains logically distinct from pointwise fixed-power Mertens but still lacks the required arithmetic estimate;
- Campaign 42 attacks the oscillatory shifted-correlation shell directly.

No proof or disproof of RH is claimed.