Finite N3 coefficient sums

Proved

D1Bound5.finiteN3_coefficient_sums

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

diophantine-tuplesnumber-theory

Integer coefficient sums computed from the actual vectors. Taking the maximum separately in each degree still leaves strict slack at4143.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.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.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteN3Height_Definitions

Formal statement

section
namespace D1Bound5















theorem _root_.D1Bound5.finiteN3_coefficient_sums (i : Fin 3) :
    ((∑ j, |(finiteN3Coeff0 i 0 j : ℝ)|)+
      (∑ j, |(finiteN3Coeff0 i 1 j : ℝ)|) ≤ 342) ∧
    ((∑ j, |(finiteN3Coeff1 i 0 j : ℝ)|)+
      (∑ j, |(finiteN3Coeff1 i 1 j : ℝ)|) ≤ 2352) ∧
    ((∑ j, |(finiteN3Coeff2 i 0 j : ℝ)|)+
      (∑ j, |(finiteN3Coeff2 i 1 j : ℝ)|) ≤ 5792) ∧
    ((∑ j, |(finiteN3Coeff3 i 0 j : ℝ)|)+
      (∑ j, |(finiteN3Coeff3 i 1 j : ℝ)|) ≤ 4096) := by sorry







end D1Bound5
end

Source

D1Bound5/FiniteN3Height.lean, lines 52-64, SHA-256 f481f700219409141bd10895fbdbd58481a503388f7da4c50027895a33e66039. Project: https://github.com/tomislav-math/d1-bound5-lean

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