Coupled phase row polynomial bound

Proved

D1Bound5.coupled_phase_row_polynomial_bound

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

All five printed phase constants follow from exact rational critical brackets. Decimal approximations are not used in the proof.

Preamble

import Mathlib.Analysis.Calculus.Deriv.MeanValue
import Mathlib.Analysis.Calculus.Deriv.Pow
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_CoupledPhaseBounds_Definitions
import Definitions.Def_D1Bound5_CoupledPhaseGeometry_Definitions

Formal statement

section
namespace D1Bound5













theorem _root_.D1Bound5.coupled_phase_row_polynomial_bound (q F : ℝ) (hrow : CoupledPhaseRow q F)
    (x : ℝ) (hx : 0 ≤ x) (hx2 : x ≤ 2) : coupledPhasePolynomial q x < F := by sorry



end D1Bound5
end

Source

D1Bound5/CoupledPhaseBounds.lean, lines 112-131, SHA-256 14ad3644c7d0af80f0ec212461e5adea70bec57470ae7e0a8a0ee48d46ce9bc9. Project: https://github.com/tomislav-math/d1-bound5-lean

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