Finite fourth-element growth certificate

Proved

D1Bound5.oneSmallFourth_34_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_25, oneSmallPairB_25, oneSmallTripleS_34, cutoff oneSmallTripleCutoff_34, and root list oneSmallDisk_300_0_5. 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_OneSmallFourthData5_Definitions
import Definitions.Def_D1Bound5_OneSmallThirdData_Definitions_002

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 12000000


















theorem _root_.D1Bound5.oneSmallFourth_34_checked :
    oneSmallFourthGrowthBool oneSmallPairA_25 oneSmallPairB_25 oneSmallTripleS_34
      oneSmallTripleCutoff_34 oneSmallDisk_300_0_5 = true := by sorry






































end D1Bound5
end

Source

D1Bound5/OneSmallFourthData5.lean, lines 51-54, SHA-256 5c4d3dbb0b4b211a60602b6817a3d1f01003ce7efb46fbb3cb9a1abbd8a8cf83. Project: https://github.com/tomislav-math/d1-bound5-lean

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