{
  "theorem": "LR Theorem C1.13",
  "proof_opens": "Taking C = c*_f(r)",
  "C_is_nonzero": true,
  "C_lives_on": "V_1, the AUXILIARY family's disc (Theorem C1.9: 'a meromorphic function on V_1 alone')",
  "uniqueness": "Remark C1.11: although g is used in the construction of omega_f, 'it is uniquely determined by f'",
  "dictionary": {
    "C": "C_pi",
    "C_d(f_beta, g, j)": "S_5(t)",
    "L_p(g tensor tau, j-1-r)": "lambda_i(t)",
    "L_p(Ad g)": "D_i",
    "log^{[r+1]}": "j(t) = log(1+t)/log_11(12)",
    "kappa(g x psi)": "z_i / the Kato class"
  },
  "every_lr_factor_matched": true,
  "every_pc001_factor_matched": true,
  "consequence": "C_pi = C = c*_f(r) is a functional of the auxiliary family alone: PARTNER-INDEPENDENT, and nonzero. RUN-090 carried this as certificate item C1's unproved core.",
  "partner_independence_label": "CITED_THEOREM",
  "label": "DERIVED_FROM_VERIFIED_INPUTS for the dictionary; CITED_THEOREM for C1.9/C1.11/C1.13",
  "agrees": true
}