Small tail parameter range

Proved

D1Bound5.small_tail_parameter_range

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

diophantine-tuplesnumber-theory

In the normalized full integral basis, a positive discriminant at most 60 forces the remaining generator coefficient to lie between 1 and 15. This stronger uniform rectangular reduction deliberately includes all 30 trace/parameter pairs, even models not needed for maximal orders.

Preamble

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Norm
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.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_Coordinates_Definitions

Formal statement

section
namespace D1Bound5


theorem _root_.D1Bound5.small_tail_parameter_range (tau nu : ℤ)
    (htau : tau = 0 ∨ tau = 1)
    (hpos : 0 < QuadInt.discriminant tau nu)
    (hcut : QuadInt.discriminant tau nu ≤ 60) :
    1 ≤ nu ∧ nu ≤ 15 := by sorry



end D1Bound5
end

Source

D1Bound5/SmallTailRange.lean, lines 6-21, SHA-256 c865f417a7e67904d3233f7fda419d37747223d0ad8cd78c1681f681b53a4c0d. Project: https://github.com/tomislav-math/d1-bound5-lean

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