{
  "C7": "PASS / canonical",
  "actual_independent_routes": 1,
  "determinant_category": "rank-1 projective R_S-modules in cohomological degree 0, both ends included",
  "kappa_det": "1",
  "why": "Det's functoriality on rank-1 projective R_S-modules: Det(Psi_4 Psi_3 Psi_2 Psi_1^{-1}) = Det(Psi_4)Det(Psi_3)Det(Psi_2)Det(Psi_1)^{-1}, one route, the same functor, the same grading, dual, localization, orientation and induced H^1 maps (Eq. 11); (18.1) applies, and (18.2) on h = id gives 1",
  "not_claimed": [
    "C9 (the residual neutral line's monodromy) and C10 - untouched as instructed",
    "the characteristic ideal of any H^2 (main-conjecture content; not a K_1 matter)",
    "v_11(q) (RUN-099: L, q_D, outside-certificate obligation)"
  ],
  "agrees": true
}