Indexed mutation-closure certificate for prepared pair 26, part 1

Proved

D1Bound5.PairGraphPrepared26.indexed_chunk128_03_part1_checked

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

diophantine-tuplesnumber-theory

For prepared pair 26, part 1, the indexed closure certificate succeeds for at most 32 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). Original global vertex list; exactly 32 aligned witness/destination rows.

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_SmallPairGraphInputs26_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs26_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData26_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData26_Definitions_003

Formal statement

section
namespace D1Bound5.PairGraphPrepared26
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairGraphPrepared26.indexed_chunk128_03_part1_checked :
    pairIndexedWitnessesPrefixBool smallPairA_26 smallPairB_26 anchorRoot
      (10^1100) smallPairClosure_26 32
      (witnesses.drop 416) (destinations.drop 416) = true := by sorry

end D1Bound5.PairGraphPrepared26
end

Source

D1Bound5/SmallPairGraphClosure26Chunk128_03Part1.lean, lines 9-14, SHA-256 28a735fc16ec08602e867f7f0695391129f0408437239f6872c8ec0edd08cc1b. Project: https://github.com/tomislav-math/d1-bound5-lean

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