# CSM_RH Paper 44 package

This package advances CSM_RH from state v1.34 to v1.35 inside Campaign 43.

Main certified results:

- exact absorption of the translated phase into the completely multiplicative twist `f_Q(n) = lambda(n) n^(iQ)`;
- exact diagonal-unitary gauge equivalence `K_Q = D_Q^* K_0 D_Q` for every fixed translated support kernel;
- phase-only generic dispersion therefore cannot gain a fixed power from the center frequency;
- the only equal-slope determinant fibres are the outer-diagonal fibres `u = u'`, whose total contribution is `O(X^(-epsilon/10+o(1)))`;
- after removing those fibres, one van der Corput differencing step changes a two-form Liouville correlation into four distinct affine Liouville forms;
- prime-harmonic pretentious distance has only `log log X` scale, so an `exp(-c D^2)` mechanism alone cannot yield a fixed power of `X`.

Campaign 43 remains open.

WL1 closes as `CLOSED_AS_ARCHIMEDEAN_GAUGE_AND_EVEN_ORDER_LIOUVILLE_BARRIER`.

Next continuation: Campaign 43 / WL2 — `LIOUVILLE_AWARE_RAMARE_EXTRACTION`.

No RH proof or disproof is claimed.