Mixed Pair Product near Quarter

Proved

D1Bound5.mixedPairProduct_nearQuarter

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

A product of a first-row and a later-row normalized root entry lies within 7/192 of one quarter. The two error radii are different.

Preamble

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 Matrix

namespace D1Bound5


theorem _root_.D1Bound5.mixedPairProduct_nearQuarter (x y : ℂ)
    (hx : ‖x - (1/2 : ℂ)‖ < (1/18 : ℝ))
    (hy : ‖y - (1/2 : ℂ)‖ < (1/64 : ℝ)) :
    ‖x*y - (1/4 : ℂ)‖ < (7/192 : ℝ) := by sorry





end D1Bound5

namespace D1Bound5



end D1Bound5

namespace D1Bound5



end D1Bound5
end

Source

D1Bound5/MixedFourDetBound.lean, lines 8-45, SHA-256 863a07b764253ce476290edc497efddecf3c39545921323e93756d8912d3da78. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph