Finite Polynomial height scalar

Proved

D1Bound5.finitePolynomial_height_scalar

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

diophantine-tuplesnumber-theory

A rational computation on the actual coefficient vector supplies the strict height margin for every T≥1000. This avoids weakening the constants by combining coordinatewise maxima from different rows.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Tactic.Convert
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring

Formal statement

section
namespace D1Bound5








theorem _root_.D1Bound5.finitePolynomial_height_scalar (k : ℕ) (v : Fin (k+1) → ℝ)
    (hv : ∀ ell, 0 ≤ v ell) (M T : ℝ) (hT : 1000 ≤ T)
    (hslack : (101/100 : ℝ)*(∑ ell, v ell/(1000 : ℝ)^(k-(ell : ℕ))) < M) :
    (101/100 : ℝ)*(∑ ell, v ell*T^(ell : ℕ)) < M*T^k := by sorry

end D1Bound5
end

Source

D1Bound5/FinitePolynomialHeight.lean, lines 51-72, SHA-256 0a57cf8e5e1b1bdad792f7fa018731c8a4bb1a5108b9cf615b3eb680734f76c5. Project: https://github.com/tomislav-math/d1-bound5-lean

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