{
  "identification": "11 ∤ #Ẽ(F_11) = 16, so E(Q_11) ⊗̂ Z_11 = E_1(Q_11) and H^1_f(Q_11,T) = E(Q_11) ⊗̂ Z_11 (Bloch–Kato, CITED)",
  "omega_expansion": "ω = (1t^0 + 0t^1 + 1t^2 + 2t^3 + …) dt",
  "log_series": "log(t) = 1t^1 + 0t^2 + 1/3t^3 + 1/2t^4 + -3/5t^5 + …",
  "cofactor": 16,
  "rows": {
    "P": {
      "v_11(t)": 1,
      "in_E_1": true,
      "v_11(log)": 1,
      "log/11 mod 11^3": 328,
      "t/11 mod 11": 9
    },
    "Q": {
      "v_11(t)": 1,
      "in_E_1": true,
      "v_11(log)": 1,
      "log/11 mod 11^3": 611,
      "t/11 mod 11": 6
    }
  },
  "valuation_theory": "log(t) = t + Σ_{n≥2} (a_n/n) t^n with a_n integral on a minimal model, and for v(t) ≥ 1, p = 11: v(t^n/n) ≥ n − log_p(n) > 1, so v(log t) = v(t) exactly",
  "v_11_of_log_omega_g": 1,
  "declared": 1,
  "image_of_the_integral_lattice": "11^1 · Z_11",
  "integrally_trivial": false,
  "index": 11,
  "rational_iso_is_not_an_integral_unit": true,
  "claimed_unit": false,
  "C6_relation": {
    "what C6 settled": "η_pdR = 1 — the period/de Rham comparison pairing ⟨γ, ω⟩ of the normalisation route (Eichler–Shimura; Ω^± is its value on the chosen Betti basis), RUN-099",
    "what this round uses": "the Bloch–Kato identification D_dR(V)/Fil⁰ ≅ Q_11 via ω_E, i.e. the formal-group logarithm of the minimal model",
    "shared": "the differential ω_E appears in both",
    "different": "one is a global Betti/de Rham comparison, the other a local p-adic Hodge identification; no theorem in this tree identifies their normalisations",
    "forbidden_inference": "η_pdR = 1 ⇒ the local log normalisation is 1",
    "inference_taken": false,
    "what_it_would_have_cost_here": "a factor 11: the integral image is 11^1 · Z_11, not Z_11"
  },
  "reading": "the local Bloch–Kato line is NOT integrally trivial: log_ω carries H^1_f(Q_11,T) onto 11^1 · Z_11. This is a local arithmetic datum of the line, not a reopening of the normalisation certificate.",
  "agrees": true
}