Finite QResidual norm lt

Proved

D1Bound5.finiteQResidual_norm_lt

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

diophantine-tuplesnumber-theory

The actual finite-Q pair residual has the manuscript's strict bound. It follows from convergent Taylor estimates, explicit cancellations, and the actual anchor moduli.

Preamble

import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteQResidualIdentity_Definitions

Formal statement

section
namespace D1Bound5








theorem _root_.D1Bound5.finiteQResidual_norm_lt
    (u v c : ℂ) (A T : ℝ) (hA : 0 < A)
    (hAu : A ≤ ‖u‖) (hAv : A ≤ ‖v‖)
    (huT : ‖u‖ ≤ T) (hvT : ‖v‖ ≤ T) (hAC : 1000 ≤ A*‖c‖) :
    ‖finiteQResidual u v c‖ < 3*T/(2*A^2*‖c‖^4) := by sorry

end D1Bound5
end

Source

D1Bound5/FiniteQResidualBound.lean, lines 96-126, SHA-256 a3e6f379d6e8b22749f6d6447d2c163488ae6d9c3b3948f32b3749f0bb7a7bac. Project: https://github.com/tomislav-math/d1-bound5-lean

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