{
  "exponents": {
    "L_p(g x psi)": {
      "Psi_4": 1,
      "Psi_1": -1
    },
    "L_p(g x tau)": {
      "Psi_3": 1,
      "Psi_1": -1
    },
    "L_p(Ad g)": {
      "Psi_3": -1,
      "Psi_1": 1
    },
    "C_d": {
      "Psi_3": 1,
      "Psi_1": -1
    },
    "log^{[r+1]}": {
      "Psi_3": 1
    },
    "X^n": {
      "Psi_2": -1
    }
  },
  "net": {
    "L_p(g x psi)": 0,
    "L_p(g x tau)": 0,
    "L_p(Ad g)": 0,
    "C_d": 0,
    "log^{[r+1]}": 1,
    "X^n": -1
  },
  "cancel_exactly": [
    "L_p(g x psi)",
    "L_p(g x tau)",
    "L_p(Ad g)",
    "C_d"
  ],
  "residual": {
    "log^{[r+1]}": 1,
    "X^n": -1
  },
  "residual_as_written": "log^{[r+1]} / X^n",
  "C_over_c_f": "alias of Psi_2's X^n extraction (C = c_f with X^n removed): counted once, not twice",
  "residual_is_the_named_extractions": true,
  "named_extractions": {
    "log^{[r+1]}": "C1.8 divides kappa-hat_d by it",
    "X^n": "the leading term at X = 0 (C1.7 area; C1.10's n)"
  },
  "reading": "every L-function cancels exactly (Eq. 11 is the cancellation) and C_d cancels; the composite is defined over H_Gamma after the two named leading-term extractions and nowhere else needs a localization"
}