{
  "rows": [
    {
      "factor": "torsion",
      "module": "E(Q)[11^∞] (rational torsion)",
      "sequence": "0 → E(Q)[11^∞] → H^1(Z_S,T)_tors: the image of H^0(Z_S,E[11^∞]) (Kummer); its dual in H~^3_ord(Q,T) ≅ H~^0(Q,E[11^∞])^∨ ⊆ H^0(Q,E[11^∞])^∨",
      "degree": 1,
      "exponent": 1,
      "source": "RUN-011 (torsion trivial)",
      "destination": "F_fin,11 (torsion endpoint)",
      "length_11": 0,
      "label": "COMPUTED_HERE"
    },
    {
      "factor": "sha",
      "module": "Sha(E/Q)[11^∞]",
      "sequence": "0 → E(Q)⊗Q_11/Z_11 → Sel_{11^∞}(E/Q) → Sha[11^∞] → 0; its dual is the torsion of H~^2_ord ≅ Sel^∨ and of H^2(Z_S,T) ≅ Sel_str^∨",
      "degree": 2,
      "exponent": -1,
      "source": "the programme's documents",
      "destination": "F_fin,11 (middle module)",
      "length_11": 0,
      "label": "INHERITED — NUMERIC ONLY"
    },
    {
      "factor": "tamagawa-389",
      "module": "Tamagawa c_389",
      "sequence": "H^1(Q_389,T)/H^1_ur(Q_389,T) and H^2(Q_389,T) = E(Q_389)[11^∞]^∨ inside RΓ_{/ur}(Q_389,T) — acyclic here",
      "degree": 2,
      "exponent": -1,
      "source": "RUN-067 (Kodaira I_1, c_389 = 1)",
      "destination": "F_fin,11 (local piece at 389)",
      "length_11": 0,
      "label": "COMPUTED_HERE"
    },
    {
      "factor": "local-11-torsion",
      "module": "E(Q_11)[11^∞] and Ẽ(F_11)[11^∞]",
      "sequence": "H^0(Q_11,T^-⊗Q/Z) = H^2(Q_11,T^+)^∨ and H^0(Q_11,E[11^∞]) = H^2(Q_11,T)^∨ — the local H^2 terms of CS (2.13) and of the ordinary local condition",
      "degree": 2,
      "exponent": -1,
      "source": "RUN-104 (11 ∤ 16)",
      "destination": "F_fin,11 (local piece at 11)",
      "length_11": 0,
      "label": "COMPUTED_HERE"
    },
    {
      "factor": "index-at-11",
      "module": "coker(loc_11: E(Q)⊗Z_11 → E(Q_11)⊗̂Z_11) = Z/11^k",
      "sequence": "the torsion of H^2(Z_S,T) ≅ Sel_str^∨ (degree 2) — and NOT again in the local line H^1_f(Q_11,T), which is torsion-free (index enters once)",
      "degree": 2,
      "exponent": -1,
      "source": "RUN-104 (depth of 16P, 16Q)",
      "destination": "H_str (its torsion part)",
      "length_11": 0,
      "label": "COMPUTED_HERE"
    },
    {
      "factor": "unramified-389",
      "module": "H^1_ur(Q_389,T) and H^1(Q_389,T)",
      "sequence": "RΓ_ur(Q_389,T) → RΓ(Q_389,T) → RΓ_{/ur}(Q_389,T): all acyclic (Z_11(1)/388 = 0; E(Q_389)[11^∞] = 0)",
      "degree": 1,
      "exponent": 1,
      "source": "RUN-104",
      "destination": "F_fin,11 (local piece at 389)",
      "length_11": 0,
      "label": "COMPUTED_HERE"
    }
  ],
  "rule": "Single-Entry: every finite factor enters through exactly one exact sequence, with its degree and sign; nothing is multiplied by hand afterwards; a free line is never filed as a finite module",
  "duplicates": [],
  "misfiled": [],
  "unplaced": [],
  "sum_of_11_lengths": 0,
  "finite_package_at_11": "the unit line: every finite module that could enter has 11-length 0 (torsion trivial, c_389 = 1, 11 ∤ #Ẽ(F_11), index 11^0; Sha[11^∞] = 0 inherited, numeric only)",
  "middle_module": "not named Sha × Tamagawa: at 11 its graded pieces are the local pieces (all zero) and the inherited Sha piece (zero, numeric only); the naming rule of Round 033 §13–14 is respected by having nothing to name",
  "B_versus_G": "B places: which module, which sequence, which degree, which sign — done; G would evaluate: the values are all zero here except the inherited one, and none of that is claimed as a theorem",
  "agrees": true
}