{
  "A": "PARTIAL",
  "route": "D (derived), but not through B_N: through Kato's Kolyvagin derivative kappa_{397*991}^Kato, which the literature ties to B_N's canonical content by theorem",
  "canonical_identification_B_N_eq_Boc_BKS": "FAIL as posed",
  "source": "kappa_{397*991}^Kato in H^1(Q, E[11]) (Kato's Euler system, Kolyvagin derivative); its canonical shadow det(loc_n) != 0",
  "theorem_identification": "Kim's semi-local theorem (nonvanishing equivalence) + Kim 3.11 (up to a unit u); no element-level identification exists in the four papers read",
  "mod_11_determinant": "nonzero: det(M_loc) = 2, delta-tilde_n != 0",
  "characteristic_zero_lift": "UNMEASURED",
  "rank_2_independence": "PASS by the determinant",
  "local_conditions": "PASS",
  "Delta_A_nonzero": {
    "mod 11": true,
    "over Q_11": "UNMEASURED"
  },
  "P5_CANON_BocID": "closed NEGATIVELY as posed (B_N is not BKS's Boc_F); re-posed as the smallest missing theorem",
  "smallest_missing_theorem": "an element-level identification: the image of Kato's Kolyvagin/Stark system at n = 397*991 under MCS's canonical isomorphism, reduced mod 11, equals det(loc_n) with the unit u of Kim 3.11 computed - equivalently BKS Conjecture 1.1(iii) at F = Q(397*991)^(11), or a Kurihara-type formula delta_n = +-det(loc_n) * (explicit unit)",
  "fallback_needed": false,
  "why_no_fallback": "the derived route already yields a mod-11 rank-2 source by theorem; the explicit BF route would be needed only for an element-level characteristic-zero determinant, which is the GPR content",
  "parallel_opportunities_noted": [
    "G: finite certificates (many inputs computed)",
    "D: reciprocity (LR/Kato chain in hand)",
    "C: regulator (symbolic Rounds 031-035 specify the target)"
  ],
  "B_to_G_untouched": true,
  "not_claimed": [
    "B_N = the BKS / Nekovar Bockstein regulator (it is not)",
    "Delta_A != 0 over Q_11",
    "IMC_11 verified here (cited, external)",
    "the value of the unit u in Kim 3.11",
    "any of B-G"
  ],
  "agrees": true
}