Small tail discriminant bound

Proved

D1Bound5.small_tail_discriminant_bound

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

The small-tail search reduces to Delta<=60 even when both entries are real. In that case their nonreal square root supplies the cutoff.

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.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_Coordinates_Definitions

Formal statement

section
namespace D1Bound5

open QuadInt













theorem _root_.D1Bound5.small_tail_discriminant_bound {tau nu : ℤ}
    (hd : 0 < QuadInt.discriminant tau nu) (b c r : QuadInt tau nu)
    (hbc : b ≠ c) (hNb : 9 ≤ b.norm) (hNbc : b.norm ≤ c.norm)
    (hNc : c.norm ≤ 15) (hr : r*r = b*c+1) : QuadInt.discriminant tau nu ≤ 60 := by sorry

end D1Bound5
end

Source

D1Bound5/FiniteTail.lean, lines 88-127, SHA-256 4a84a3e4ca3b7d43920e93e12f04cbea329f4d21bc5572c8337e09d252793110. Project: https://github.com/tomislav-math/d1-bound5-lean

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