Bennett two height normalization

Proved

D1Bound5.bennett_two_height_normalization

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

diophantine-tuplesnumber-theory

The exact local coefficient majorant, after multiplication by the integral clearing factor, has exponential base strictly below 42. All geometric and scale hypotheses are elementary real inequalities; no bound on the coefficient being estimated occurs among the assumptions.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Tactic.FieldSimp
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.bennett_two_height_normalization
    (X Y δ B C N U r : ℝ) (k : ℕ)
    (hX : 0 < X) (hY : 0 < Y) (hδ : 0 < δ)
    (hB : 0 < B) (hC : 0 < C) (hXB : X ≤ B)
    (hδB : δ ≤ X+B) (hN : N = X*Y*C)
    (hscale : 1000 ≤ N/B) (hUlo : N-X ≤ U) (hUhi : U ≤ N+X)
    (hradius : r = 2*min X δ/5) (hk : 1 ≤ k) :
    (4*X*Y*δ^2)^k * ((U+r)/U) *
        ((U+r)/(r*(X-r)*(δ-r)))^k < (42*Y^2*B*C)^k := by sorry

end D1Bound5
end

Source

D1Bound5/BennettHeightNormalization.lean, lines 40-147, SHA-256 b5e61e5d6eb88e26d2647369bff77c509498654f629d2229d692762546241a03. Project: https://github.com/tomislav-math/d1-bound5-lean

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