Pair Phase Pilot41 — closure checked by indexed witness

Proved

D1Bound5.PairPhasePilot41.closure_checked_by_indexed_witness

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

diophantine-tuplesnumber-theory

Auxiliary result PairPhasePilot41.closure_checked_by_indexed_witness in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

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_PairExtensionCore_Definitions
import Definitions.Def_D1Bound5_SmallPairPhaseData41_Definitions

Formal statement

section
namespace D1Bound5.PairPhasePilot41
set_option maxRecDepth 100000
set_option maxHeartbeats 0





theorem _root_.D1Bound5.PairPhasePilot41.closure_checked_by_indexed_witness :
    pairClosureBool anchorA anchorB (10^1100) closure = true := by sorry

end D1Bound5.PairPhasePilot41
end

Source

D1Bound5/SmallPairIndexedClosure41.lean, lines 390-393, SHA-256 aa955931a4521c8735423353db9d089a97667a50300a9fb2f5aca1b3277b29ee. Project: https://github.com/tomislav-math/d1-bound5-lean

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