{
  "psi": "χ₈·χ_cyc — the second Jordan–Hölder character (RUN-091)",
  "ordering": "0 → ψ → V_Eis → 1 → 0",
  "matrix": "ρ(g) = (ψ(g) c(g); 0 1)",
  "which_entry_is_the_class": "the upper-right entry c(g)",
  "basis_frame": "e₁ spans the sub; e₂ is any lift of the quotient — the class is independent of that lift",
  "cocycle_identity": "c(gh) = ψ(g)c(h) + c(g)",
  "extension_group": "Ext¹(1, ψ) = H^1(Q, Q_11(chi_8)(1))",
  "is_the_target_line": true,
  "matrix_product_forces_the_cocycle": true,
  "lift_change_is_a_coboundary": true,
  "split_iff_coboundary": true,
  "trials": 40,
  "modulus": "Z/11^4",
  "lifting_status": "the identities are verified integrally over Z/11ⁿ for every n tested; no class is exhibited, so no lifting question arises yet — what is fixed here is the dictionary",
  "agrees": true
}