# CSM_RH Paper 08 v0.1

Campaign 07 pins one exact Vaughan identity and applies it to the zero-frequency CSSA paraproduct.

Main results:

- the short block is `N^(5/3+o(1))` and harmless;
- the two Type-I blocks, the Type-II block, and the centering block are all critical at `N^(3+o(1))` under coefficient-blind estimates;
- their exact signed recombination is the original long CSSA target;
- the first Type-I block contains an unattenuated `d=1` zero-frequency atom;
- standard blockwise Type-I/II triangle estimation gives zero fixed-power frontier contraction;
- the Vaughan instance of GZMPS remains open;
- Campaign 08 fixes the Heath-Brown identity at K=3 and tests whether the alternating higher-convolution structure cancels low-order unit configurations before estimation.

No proof or disproof of RH is claimed.
No live GLM provider run is claimed.