One Small Cutoff Rows finite N2Fixed Bound
ProvedD1Bound5.oneSmallCutoffRows_finiteN2FixedBounddiophantine-tuplesnumber-theory
Each of the57 actual cutoff triples has exact coefficient-square certificates for the manuscript's M2, computed from the proved N2 integer coefficient vectors.
Preamble
import Lean.Elab.Tactic.Omega import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Data.List.Range import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.Tactic.FinCases import Mathlib.Tactic.GCongr import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Positivity import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_001 import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_002 import Definitions.Def_D1Bound5_OneSmallN2FixedArithmetic_Definitions
Formal statement
section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.oneSmallCutoffRows_finiteN2FixedBound (r : OneSmallCutoffRow)
(hr : r ∈ oneSmallCutoffRows) :
∃ w : Fin 3 → Fin 2 → Fin 3 → ℚ, FiniteN2FixedBound r w := by sorry
end D1Bound5
end
Source
D1Bound5/OneSmallN2FixedArithmetic.lean, lines 436-500, SHA-256 164624a5c23628e859c312cd4e25138d33e47f04cca6c8177425d4c89d42a3cd. Project: https://github.com/tomislav-math/d1-bound5-lean