{
  "chain": [
    {
      "step": "Kato's zeta element z_{Q(zeta_n)}",
      "source": "Kato [Kat04]; Kim section 2.3",
      "status": "canonical"
    },
    {
      "step": "Kolyvagin derivative D_n z -> kappa_n^Kato in H^1(Q, E[11]), n = 397*991",
      "source": "Kim section 2.3 (Mazur-Rubin's construction)",
      "status": "canonical"
    },
    {
      "step": "res_p then exp*_{omega_E}: kappa_n^Kato -> u * delta-tilde_n",
      "source": "Kim Thm 3.11 / CS Thm 2.1.3",
      "status": "up to the unit u"
    },
    {
      "step": "delta-tilde_n != 0 (computed)",
      "source": "RUN-068 (src70): 5 in the disclosed normalisation; every unit reachable by root choice (RUN-069)",
      "status": "COMPUTED"
    },
    {
      "step": "=> kappa_n^Kato != 0, and loc_n : Sel(Q,E[11]) -> (+) E(F_l)(x)F_11 is an isomorphism",
      "source": "Kim's semi-local theorem",
      "status": "theorem, hypotheses instantiated"
    },
    {
      "step": "<=> det(M_loc) != 0 (computed: 2)",
      "source": "RUN-011 / RUN-067 (src12, src69)",
      "status": "COMPUTED"
    },
    {
      "step": "= the canonical content of B_N: [det loc_n] in P(det)",
      "source": "this round",
      "status": "identification of LINES; the coefficient is a gauge"
    }
  ],
  "delta_mod_11": 5,
  "delta_nonzero": true,
  "what_the_chain_is": "an equivalence of nonvanishing plus an up-to-unit scalar identity; NOT a commutative diagram identifying B_N with a Bockstein map of a complex",
  "element_level_identification": "absent",
  "agrees": true
}