{
  "node": "RH-ModulatedPairingUniformity v3.12",
  "decisions": {
    "UMP4": "FALSE",
    "averaged_UMP4": "FALSE",
    "global_Wick_centering_on_parallelogram": "MISALIGNED",
    "constraint_adapted_centering": "REQUIRED"
  },
  "exact_counterexample": {
    "conductor": 2,
    "modulation": "lambda=1/2",
    "pointwise_remainder_scale": "Theta(H^4)",
    "character_averaged_remainder_scale": "Theta(H^3)"
  },
  "constraint_adapted_decomposition": {
    "axis": "A_q(d)=mu_q(d)^2-(A(q)-1)",
    "axis_free": "K4_perp=K4-A_q(d)",
    "K4_perp_alpha_zero_axis": 0,
    "K4_perp_beta_zero_axis": 0,
    "K4_perp_symmetric": true
  },
  "automatic_reject": [
    "UMP4 or averaged UMP4",
    "local shift-uniform lemmas promoted to global shift-uniform pairing theorem",
    "all three Wick channels separated before constrained centering",
    "pairing channels bounded independently by absolute value",
    "axis-free mixed Sobolev numerics promoted as theorem"
  ],
  "next_node": "RH-Parallelogram-ConstraintAdaptedPairing v3.13",
  "trust": {
    "rh_claim": false,
    "eta_M_positive_proved": false,
    "eta_Q_positive_proved": false
  }
}