Fixed cutoff start above Q
ProvedD1Bound5.fixed_cutoff_start_above_Qdiophantine-tuplesnumber-theory
Scalar conversion of the first overlap, retaining every strict inequality. The two growth premises are precisely the actual retained bounds already proved for fixed triples.
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.Data.List.Range import Mathlib.Data.Real.Basic import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination
Formal statement
section
namespace D1Bound5
theorem _root_.D1Bound5.fixed_cutoff_start_above_Q (K S T C D : ℝ)
(hK : 0 < K) (hS : 0 < S) (hT : 0 < T) (hC : 0 < C)
(hgap : K*T^5/S^2 < C) (hstart : C^7/(S^2*T^4) < D)
(hover : 1 < (1-1/4000 : ℝ)*K^4*T^10/(12100*S^10)) :
4*55^2*T^6*C^3/(1-1/4000 : ℝ) < D := by sorry
end D1Bound5
end
Source
D1Bound5/OneSmallCutoffReal.lean, lines 43-74, SHA-256 cfc21933cb4a82de4a9d5409cd9e6c6bc2d0d33f2b3a2f409c936a0b91b57d93. Project: https://github.com/tomislav-math/d1-bound5-lean