# CSM_RH Paper 37 v0.1

Campaign 36 activates a minimal fixed-power breakthrough gate.

Main results:
- a fixed-power arithmetic theorem is not admitted unless its observable sees the RH-hard dyadic prime-error mode and has a proved bridge to PESC/MLEPG;
- the known quotient-transform von-Mangoldt theorem has a genuine ~x^0.47179 error but fails dyadic observability;
- exact countermodel: g_X=1 on (X,2X] has quotient transform identically 1 on that dyadic block while its cumulative mass is X;
- current PESC, MLEPG, Guth-Maynard, Gafni-Tao, principal-Fejer and recurrence families do not yet supply an admitted fixed exponent;
- Gafni-Tao's exceptional-set theorem fixes the relative threshold delta and does not authorize delta=X^-eta;
- a new deterministic bridge is certified: a power-sized exceptional set at a polynomially shrinking relative threshold immediately implies fixed-power lag energy and hence MLEPG;
- no theorem is admitted in Campaign 36;
- Campaign 37 attacks threshold dependence in the Gafni-Tao/Guth-Maynard machinery directly.

No proof or disproof of RH is claimed.