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Fixed cutoff start above Q

Proved
D1Bound5.fixed_cutoff_start_above_Q

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

diophantine-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

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