Finite fourth-element growth certificate

Proved

D1Bound5.oneSmallFourth_42_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_31, oneSmallPairB_31, oneSmallTripleS_42, cutoff oneSmallTripleCutoff_42, and root list oneSmallDisk_300_1_3. 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_OneSmallFourthData6_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_42_checked :
    oneSmallFourthGrowthBool oneSmallPairA_31 oneSmallPairB_31 oneSmallTripleS_42
      oneSmallTripleCutoff_42 oneSmallDisk_300_1_3 = true := by sorry






































end D1Bound5
end

Source

D1Bound5/OneSmallFourthData6.lean, lines 51-54, SHA-256 7aac959f93eca3ae2cb1239543f66f1845a1dfb068e2493999adf9be5e60d0a6. Project: https://github.com/tomislav-math/d1-bound5-lean

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