{
  "node": "RH-CenteredShift-FourierGap v3.6",
  "canonical_gate": {
    "name": "QEGC_eta",
    "object": "genuine four-distinct equal-gap covariance Q_N",
    "condition": "|Q_N| << N^(5-eta+o(1))",
    "range": "0 < eta < 1",
    "translation": {
      "shift_variance": "V_N << N^(5-eta+o(1))",
      "PNT_mean_square": "I(N) << N^(3-eta/2+o(1))",
      "zero_strip": "Theta <= 1-eta/4"
    }
  },
  "quartic_partition": {
    "same_pair_diagonal": "O(N^(4+o(1)))",
    "shared_index_semidiagonal": "O(N^(4+o(1)))",
    "genuine_four_distinct": "only N^5-capable family"
  },
  "model_aware_gate": {
    "offsets": "{0,h,d,d+h}",
    "refined_singular_series": "S0",
    "covariance_backbone": "K4(h,d)=S0(0,h,d,d+h)-(S(h)-1)^2",
    "required_subtasks": [
      "bound constrained refined-singular-series aggregate M_4,N",
      "bound actual prime deviation E_4,N"
    ]
  },
  "automatic_reject": [
    "diagonal-only quartic improvement",
    "semi-diagonal-only quartic improvement",
    "pair centering treated as four-point independence",
    "generic four-tuple singular-series average applied directly to parallelogram tuples",
    "logarithmic N^5/log^A saving promoted as fixed eta",
    "large-value or zero-density theorem with no Q_N translation",
    "finite N^4 log^2 numerical behavior promoted as theorem"
  ],
  "next_node": "RH-RefinedSingularSeries-Parallelogram v3.7",
  "trust": {
    "rh_claim": false,
    "eta_Q_positive_proved": false,
    "K4_sample_is_numerical_only": true
  }
}