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Near Half triple cofactor bound

Proved
D1Bound5.nearHalf_triple_cofactor_bound

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Uniform diagonal cofactor error for three entries near one half.

Preamble
import Lean.Util.CollectAxioms
import Mathlib.Analysis.CStarAlgebra.Matrix
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.LinearAlgebra.Matrix.Permutation
import Mathlib.LinearAlgebra.Matrix.SchurComplement
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring

Formal statement
section
open scoped Matrix.Norms.L2Operator
open Matrix

namespace D1Bound5







end D1Bound5


namespace D1Bound5





end D1Bound5

namespace D1Bound5


theorem _root_.D1Bound5.nearHalf_triple_cofactor_bound (x y z : ℂ)
    (hx : ‖x - (1/2 : ℂ)‖ < (128/8649 : ℝ))
    (hy : ‖y - (1/2 : ℂ)‖ < (128/8649 : ℝ))
    (hz : ‖z - (1/2 : ℂ)‖ < (128/8649 : ℝ)) :
    ‖2*x*y*z - (1/4 : ℂ)‖ < (23/1000 : ℝ) := by sorry

end D1Bound5
end
Source
D1Bound5/AdjugateFourBounds.lean, lines 112-180, SHA-256 e5781cd0cc609ab6e464413c644de534702a0bca3e48c68b9e060b00a6b88c13. Project: https://github.com/tomislav-math/d1-bound5-lean

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