Finite fourth-element growth certificate

Proved

D1Bound5.oneSmallFourth_11_checked

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

diophantine-tuplesnumber-theory

The finite fourth-element growth check succeeds for anchors oneSmallPairA_7, oneSmallPairB_7, oneSmallTripleS_11, cutoff oneSmallTripleCutoff_11, and root list oneSmallDisk_300_0_2. Every tested candidate below this cutoff that passes the three square conditions satisfies N(z) ≤ 4N(b)N(s).

Preamble

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
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.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_OneSmallDisks_Definitions
import Definitions.Def_D1Bound5_OneSmallFiniteCheck_Definitions
import Definitions.Def_D1Bound5_OneSmallFourthData2_Definitions
import Definitions.Def_D1Bound5_OneSmallThirdData_Definitions_001

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 12000000

























theorem _root_.D1Bound5.oneSmallFourth_11_checked :
    oneSmallFourthGrowthBool oneSmallPairA_7 oneSmallPairB_7 oneSmallTripleS_11
      oneSmallTripleCutoff_11 oneSmallDisk_300_0_2 = true := by sorry































end D1Bound5
end

Source

D1Bound5/OneSmallFourthData2.lean, lines 71-74, SHA-256 9bdd844e1a1dd93e94c0a25cded3a92f3e641f7528cfe2a1a7e6a8d500bc3593. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph