{
  "node": "RH-MeanSquare-ArithmeticGap v3.5",
  "main_target": "I(X) << X^(3-kappa+o(1))",
  "gate_A": {
    "name": "minimal_signed_aggregate",
    "condition": "|sum_h R_N(h)| << N^(3-kappa+o(1))",
    "translation": "kappa -> Theta <= 1-kappa/2"
  },
  "gate_B": {
    "name": "centered_shift_L2",
    "condition": "sum_h |R_N(h)|^2 << N^(5-eta+o(1))",
    "translation": "kappa=eta/2; Theta <= 1-eta/4"
  },
  "gate_C": {
    "name": "Chou_prime_pair_error_variance",
    "condition": "E_pair(N) << N^(3-eta)",
    "translation": "Theta <= 1-eta/2",
    "source": "Chou-Haag-Huryn-Ledoan, JNT 278 (2026)"
  },
  "required_centering": {
    "sequence": "a_n = Lambda(n)-1",
    "shift_backbone": "(singular_series(h)-1) W_N(h)"
  },
  "automatic_reject": [
    "raw shift variance without singular-series subtraction",
    "logarithmic or subpower saving promoted as fixed kappa",
    "diagonal-only improvement promoted as first strip progress",
    "zero-density estimate that allows one rightmost exceptional zero",
    "finite numerical shift cancellation promoted as tail theorem",
    "new RH-equivalent representation without arithmetic saving"
  ],
  "next_node": "RH-CenteredShift-FourierGap v3.6",
  "trust": {
    "rh_claim": false,
    "eta_shift_positive_proved": false,
    "kappa_positive_proved": false
  }
}