Indexed mutation-closure certificate for prepared pair 26

Proved

D1Bound5.PairGraphPrepared26.indexed_chunk128_03_checked

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

diophantine-tuplesnumber-theory

For prepared pair 26, the indexed closure certificate succeeds for at most 128 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 and original global destination indices are preserved.

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_checked :
    pairIndexedWitnessesPrefixBool smallPairA_26 smallPairB_26 anchorRoot
      (10^1100) smallPairClosure_26 128
      (witnesses.drop 384) (destinations.drop 384) = true := by sorry

end D1Bound5.PairGraphPrepared26
end

Source

D1Bound5/SmallPairGraphClosure26Chunk128_03.lean, lines 11-36, SHA-256 3f8b5c5e0e99be7caf3d54a5c35bc20b179e5c1f8af872bd340d2a65173c3838. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph