{
  "C_pi": "c_lead / q_f",
  "constituents": {
    "c_lead": {
      "source": "LR Thm C1.9: c_f(k) is a meromorphic function on V_1 alone",
      "side": "auxiliary",
      "canonical": true
    },
    "q_f": {
      "source": "PC-001 section 4 = LR section A8.3: b_f^+(0) = c_r eta_f, a trivialisation of D_cris(F^+ D(f)^*(-1-k)), a module built from f alone",
      "side": "auxiliary",
      "canonical": false
    }
  },
  "sides": {
    "c_lead": "auxiliary",
    "q_f": "auxiliary"
  },
  "every_constituent_auxiliary_only": true,
  "partner_enters_only_through": [
    "eta_g"
  ],
  "non_canonical_constituents": [
    "q_f"
  ],
  "nonvanishing_source": "C1.13",
  "c19_nonvanishing_excepts_k_equals_r": true,
  "nonvanishing_note": "our point is k = r, which is exactly the weight C1.9's non-vanishing clause excepts; the nonvanishing comes from C1.13's c*_f(r) in L^x instead",
  "pc001_text": {
    "writes_C_pi_as_c_lead_over_q_f": true,
    "refuses_to_assume_q_f_is_1": true,
    "calls_the_common_frame_a_necessary_assumption": true,
    "says_the_factor_cancels_in_(2)": true
  },
  "conclusion": "every constituent of C_pi is auxiliary-only, so no property of either partner can obstruct fixing one frame: the common frame PC-001 calls a necessary assumption is a free, partner-independent normalisation. b_f^+ is non-canonical (section A8.3), so C_pi has no numerical value until one trivialisation is fixed, and anything built from C_aux inherits that ambiguity.",
  "common_frame_has_a_partner_dependent_obstruction": false,
  "agrees": true
}