{
  "scaling": "Omega^+- -> (w+, w-) Omega^+-, a change of B2.1's chosen Betti bases; exponents (e+, e-) mean x -> (w+)^e+ (w-)^e- x",
  "read_off_the_source": {
    "L_p(g x chi)": "B2.2, exponent -1 in the sign's period, sign = (-1)^j chi(-1)",
    "L_p(Ad g)": "B2.3, exponents (-1, -1)",
    "c_f": "C1.9, (0, 0)"
  },
  "forced_by_invariance": {
    "eta_g": "Col linear in eta_g, kappa_d canonical, Col = c_f C_d L_p^g (C1.9)",
    "kappa (i)": "C1.13's left side canonical; C, C_d, log frame-free",
    "kappa (ii)": "Kato's reciprocity Col(kappa) = L_p(g x psi), exact given gamma (B2.2)"
  },
  "laws_(w_plus_exp, w_minus_exp)": {
    "L_p(g x psi)": [
      -1,
      0
    ],
    "L_p(g x tau)": [
      0,
      -1
    ],
    "L_p(Ad g)": [
      -1,
      -1
    ],
    "L_p^g": [
      0,
      0
    ],
    "c_f": [
      0,
      0
    ],
    "Col": [
      0,
      0
    ],
    "eta_g": [
      0,
      0
    ],
    "kappa from C1.13": [
      -1,
      0
    ],
    "kappa from Kato": [
      -1,
      0
    ],
    "C1.13 RHS with Kato's kappa": [
      0,
      0
    ],
    "Psi_4 scalar": [
      0,
      0
    ]
  },
  "single_valued": true,
  "trials": 40,
  "L_p_g_frame_independent": true,
  "eta_g_frame_independent": true,
  "kappa_inverse_to_Omega_plus": true,
  "two_forcings_of_kappa_agree": true,
  "psi4_reciprocity_frame_independent": true,
  "remark": "kappa ~ (Omega^+)^{-1} says kappa is linear in the Betti class whose period is Omega^+: Kato's z_gamma is linear in gamma",
  "agrees": true
}