{
  "comparison_field": "Q(√5)",
  "rows": {
    "3": {
      "char2_chi8": -3,
      "char2_comparison": -3,
      "X_over_char2_chi8": 847,
      "X_over_char2_comparison": 847,
      "log_11": 847,
      "same": true
    },
    "7": {
      "char2_chi8": 7,
      "char2_comparison": -7,
      "X_over_char2_chi8": 220,
      "X_over_char2_comparison": 220,
      "log_11": 220,
      "same": true
    },
    "13": {
      "char2_chi8": -13,
      "char2_comparison": -13,
      "X_over_char2_chi8": 374,
      "X_over_char2_comparison": 374,
      "log_11": 374,
      "same": true
    },
    "17": {
      "char2_chi8": 17,
      "char2_comparison": -17,
      "X_over_char2_chi8": 935,
      "X_over_char2_comparison": 935,
      "log_11": 935,
      "same": true
    },
    "19": {
      "char2_chi8": -19,
      "char2_comparison": 19,
      "X_over_char2_chi8": 517,
      "X_over_char2_comparison": 517,
      "log_11": 517,
      "same": true
    },
    "23": {
      "char2_chi8": 23,
      "char2_comparison": -23,
      "X_over_char2_chi8": 1111,
      "X_over_char2_comparison": 1111,
      "log_11": 1111,
      "same": true
    },
    "29": {
      "char2_chi8": -29,
      "char2_comparison": 29,
      "X_over_char2_chi8": 517,
      "X_over_char2_comparison": 517,
      "log_11": 517,
      "same": true
    }
  },
  "jet_direction_is_the_cyclotomic_class": true,
  "what_the_jet_is": "char₂ ⊗ (log₁₁ ∘ χ_cyc) — the X-derivative of the character χ₈·χ_cyc^{1+X}, a deformation WITHIN the reducible locus; it lies in H¹(Q, Q₁₁) ≅ Hom(G_Q, Q₁₁)",
  "what_kappa_epsilon_is": "a class in H¹_f(Q, Q₁₁(χ₈)(1)), specific to Q(√2)",
  "same_group": false,
  "conclusion": "the trace jet is NOT the Kummer class: different groups, and the jet is blind to the quadratic field while κ(ε) is not. Refuted on type grounds, not by a numerical mismatch.",
  "agrees": true
}