Finite MDivided Matrix root height

Proved

D1Bound5.finiteMDividedMatrix_root_height

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

diophantine-tuplesnumber-theory

The complete actual divided M matrix satisfies a deliberately generous height bound. This avoids the manuscript's sharper geometric row estimates, while leaving ample room in its stated approximation constant.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteMMatrix_Definitions

Formal statement

section
namespace D1Bound5








theorem _root_.D1Bound5.finiteMDividedMatrix_root_height (a b s c : ℂ)
    (hB : 1 ≤ ‖b‖) (hab : ‖a‖ ≤ ‖b‖) (hbs : ‖b‖ ≤ ‖s‖)
    (hC : 1 ≤ ‖c‖) (i : Fin 4) :
    (∑ j : Fin 3, ‖finiteMDividedMatrix a b s c i j.succ‖) ≤
      169728*‖b‖^3*‖s‖^8*‖c‖^2 := by sorry

end D1Bound5
end

Source

D1Bound5/FiniteMHeight.lean, lines 89-125, SHA-256 6928941a5a34ad2fa5a5df87a96078a75cfb91e880665ed0fbfc978d07ef85b6. Project: https://github.com/tomislav-math/d1-bound5-lean

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