Indexed mutation-closure certificate for prepared pair 37

Proved

D1Bound5.PairGraphPrepared37.indexed_chunk09_checked

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

diophantine-tuplesnumber-theory

For prepared pair 37, 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). Full original vertex list and both signs; only aligned row lists are sliced.

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.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_PairClosureIndexedChunks_Definitions
import Definitions.Def_D1Bound5_PairClosureWitness_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs37_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs37_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData37_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData37_Definitions_003

Formal statement

section
namespace D1Bound5.PairGraphPrepared37
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairGraphPrepared37.indexed_chunk09_checked :
    pairIndexedWitnessesPrefixBool smallPairA_37 smallPairB_37 anchorRoot
      (10^1100) smallPairClosure_37 64
      (witnesses.drop 576) (destinations.drop 576) = true := by sorry

end D1Bound5.PairGraphPrepared37
end

Source

D1Bound5/SmallPairGraphClosure37Chunk09.lean, lines 9-14, SHA-256 257de1c2259d0c048e8ed4fee4c80e2b1d5c9214c63f777e4065a48103a61633. Project: https://github.com/tomislav-math/d1-bound5-lean

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