Full ring nonpositive integer squares common parameter

import Mathlib.Algebra.Polynomial.Monic
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Algebra.Squarefree.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Data.Finset.Card
import Mathlib.Data.Fintype.EquivFin
import Mathlib.Data.Int.GCD
import Mathlib.Data.Int.Sqrt
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination

section
open scoped NumberField
open Module

namespace D1Bound5






theorem _root_.D1Bound5.full_ring_nonpositive_integer_squares_common_parameter
    {K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
    (hK : finrank ℚ K = 2) :
    ∃ d : ℤ, 0 < d ∧ ∀ m : ℤ, m ≤ 0 →
      (∃ r : 𝓞 K, r*r = (m : 𝓞 K)) → ∃ y : ℤ, m = -d*y^2 := by sorry

























end D1Bound5
end