Finite fourth-element growth certificate

Proved

D1Bound5.oneSmallFourth_9_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_5, oneSmallPairB_5, oneSmallTripleS_9, cutoff oneSmallTripleCutoff_9, and root list oneSmallDisk_300_0_1. 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_9_checked :
    oneSmallFourthGrowthBool oneSmallPairA_5 oneSmallPairB_5 oneSmallTripleS_9
      oneSmallTripleCutoff_9 oneSmallDisk_300_0_1 = true := by sorry













































end D1Bound5
end

Source

D1Bound5/OneSmallFourthData2.lean, lines 31-34, SHA-256 9bdd844e1a1dd93e94c0a25cded3a92f3e641f7528cfe2a1a7e6a8d500bc3593. Project: https://github.com/tomislav-math/d1-bound5-lean

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