{
  "A": "PASS",
  "route": "CITED_THEOREM",
  "sub": {
    "kato_determinant_imc": "PASS/CITED_THEOREM",
    "canonical_determinant_line": "PASS",
    "distinguished_element": "PASS (unique by Remark 2.2.1, a basis, nonzero)",
    "core_rank": 1,
    "placement": "𝔷_{Q_inf}(1) is a Z_11-basis of Z_11 (P ∧ Q) (x) Sel_str(T): the rank-2 determinant tensored with the strict-Selmer line (degrees [2, -1]; conditional on the inherited Sha[11] = 0 for the numbers, unconditional in shape)",
    "stark_image": "PASS (basis of SS_1(E[11], F_can, P_1); Theorem 3.4 CITED, its hypotheses verified)",
    "A_char0": "PASS/CITED_THEOREM",
    "A_mod11_compat": "UNMEASURED"
  },
  "the_element": "Delta_A^{char 0} = 𝔷_{Q_inf}(1) ∈ det^{-1}_{Z_11} RΓ(Z_S,T) = Z_11 (P∧Q) (x) Sel_str(T); Delta_A^{mod 11} = epsilon_1 ∈ SS_1(E[11], F_can)",
  "outcome_read": "A PASS by cited theorem: the determinantal Kato main conjecture holds at (389.a1, 11) by [Wan15, BCS25] through CS Thm B and Prop 2.2.3; the determinant line is canonical; the distinguished element is unique, a basis, nonzero; its placement at the trivial character is computed, not forced",
  "explicit_vectors_demanded": false,
  "judged_on_mod11_equality": false,
  "B_to_G_untouched": true,
  "D_and_G_closed_this_round": true,
  "not_claimed": [
    "the value of the unit epsilon (𝔷_{Q_inf}(1) = epsilon · (P∧Q) (x) R_str) - not computed",
    "epsilon_1 = [det loc_{397*991}] or any equality between the Stark line and B_N's line",
    "the main conjecture re-proved here (cited: Wan15, BCS25, Kato)",
    "Sha(E/Q)[11] = 0 verified here (inherited)",
    "the internal hypotheses of Wan15 / BCS25 / Kato 12.4(1) / MR04-BSS19 core-vertex existence",
    "the Manin constant or optimality",
    "a rank-2 Stark module (the core rank is 1)",
    "any of B, C, D, E, F, G",
    "BSD"
  ],
  "agrees": true
}