{
  "source": "𝔷_{Q∞}(1) ∈ det^{-1}_{Z_11}RΓ(Z_S,T), a basis (RUN-104)",
  "first_form": "𝔷_{Q∞}(1) = ε · (P∧Q) ⊗ R_str  with  Δ_B := P∧Q a generator of D_MW,11,  σ_str := ε·R_str a generator of H_str = Sel_str(T),  φ_fin := 1 (the finite package is the unit line)",
  "second_form": "under H_str ≅ D_MW,11 ⊗ H^1_f(Q_11,T)^{-1}: 𝔷_{Q∞}(1) = ε · (P∧Q)^{⊗2} ⊗ g^{-1}, g a generator of H^1_f(Q_11,T) = E(Q_11)⊗̂Z_11, with (P∧Q)⊗g^{-1} ↦ a_Q·P − a_P·Q = R_str (mod 11: 6P − 9Q)",
  "Delta_B_nonzero": true,
  "sigma_str_nonzero": true,
  "finite_element": "1 — a determinant class of the unit line",
  "orientation": "P∧Q versus Q∧P is a sign, absorbed into ε; not an obstruction",
  "sign_treated_as_obstruction": false,
  "scalar": "ε ∈ Z_11^× UNMEASURED — not scalarised; no height is applied to σ_str (that is C)",
  "line_versus_element": "the line isomorphism Φ_B is an isomorphism of rank-one lattices; it is not an equality of scalars, and ε is what it does not determine",
  "line_iso_read_as_scalar": false,
  "transported": true,
  "agrees": true
}