Indexed mutation-closure certificate for prepared pair 19

Proved

D1Bound5.PairGraphPrepared19.indexed_chunk01_checked

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

diophantine-tuplesnumber-theory

For prepared pair 19, the indexed closure certificate succeeds for at most 64 supplied witness rows. For each row, the two supplied square roots are checked and both signed mutations are verified either by an exact lookup in the complete original vertex list or by a norm strictly exceeding (10^1100). Both mutation signs use the complete original destination vertex list.

Preamble

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.GCD
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.ZMod.Basic
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_PairClosureIndexedChunks_Definitions
import Definitions.Def_D1Bound5_PairClosureWitness_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs19_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs19_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData19_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData19_Definitions_003

Formal statement

section
namespace D1Bound5.PairGraphPrepared19
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairGraphPrepared19.indexed_chunk01_checked :
    pairIndexedWitnessesPrefixBool smallPairA_19 smallPairB_19 anchorRoot
      (10^1100) smallPairClosure_19 64
      (witnesses.drop 64) (destinations.drop 64) = true := by sorry

end D1Bound5.PairGraphPrepared19
end

Source

D1Bound5/SmallPairGraphClosure19Chunk01.lean, lines 9-14, SHA-256 ca040b32e8afbde4a0edd9ab8b8b20ee788c3992ee4f74e8058ee8b6f95cc7ba. Project: https://github.com/tomislav-math/d1-bound5-lean

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