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Exists root error three

Proved
D1Bound5.exists_root_error_three

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

diophantine-tuplesnumber-theory

First-row entries in the A >= 1, B >= 3 determinant argument.

Preamble
import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring

Formal statement
section
namespace D1Bound5









theorem _root_.D1Bound5.exists_root_error_three (x t : ℂ)
    (hx : 3 ≤ ‖x‖) (ht : t^2 = x*(x+1)) :
    ∃ v : ℂ, (v=t ∨ v=-t) ∧
      ‖v-x‖ < (5/9 : ℝ) ∧
      ‖(v-x)-(1/2 : ℂ)‖ < (25/486 : ℝ) := by sorry



end D1Bound5
end
Source
D1Bound5/RootErrorMagnitude.lean, lines 139-154, SHA-256 090472365e3db009e37be35676f898eae037822776991930233fc88ea690af2b. Project: https://github.com/tomislav-math/d1-bound5-lean

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