Reference inverse error norm lt one

Proved

D1Bound5.reference_inverse_error_norm_lt_one

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

diophantine-tuplesnumber-theory

The sharp reference inverse norm makes the normalized correction a strict contraction when all pair products have modulus at least nine.

Preamble

import Mathlib.Analysis.CStarAlgebra.Matrix
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
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
import Definitions.Def_D1Bound5_ReferenceMatrixSpectral_Definitions
import Definitions.Def_D1Bound5_RootMatrixOperatorBound_Definitions

Formal statement

section
open scoped Matrix.Norms.L2Operator
open Matrix

namespace D1Bound5




















theorem _root_.D1Bound5.reference_inverse_error_norm_lt_one
    (F : Matrix (Fin 4) (Fin 4) ℂ)
    (hnear : ‖F - halfOffDiagonal‖ < 3 * (128/8649 : ℝ)) :
    ‖halfOffDiagonalInverse * (F - halfOffDiagonal)‖ < 1 := by sorry

end D1Bound5
end

Source

D1Bound5/ReferenceInverseNorm.lean, lines 88-101, SHA-256 53050c6b49ff7b7eabf281a545ecf66dea734cd088fd701c36f0829189368aeb. Project: https://github.com/tomislav-math/d1-bound5-lean

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