Convex model symplectic contact frame pairing

Proved

BirkhoffGlobalSection.convex_model_symplectic_contact_frame_pairing

by Mazecto · Oct 3, 2026 · Mathlib 0df444a (Lean v4.33.1)

convex-geometryreal-analysis

The normalized convex model symplectic contact-frame pair has unit weighted exterior pairing with the stated orientation convention.

All displayed regularity, tangency, normalization and supplied-data hypotheses of the exact formal statement are retained. This is a conditional result for the defined convex regularization model, not a global-section or index-existence theorem.

Preamble

import Theorems.Thm_BirkhoffGlobalSection_contact_frame_basis_bundle
open BirkhoffGlobalSection Set Filter SignType
open scoped ContDiff Topology
set_option linter.unusedVariables false


set_option autoImplicit false
set_option maxHeartbeats 800000

Formal statement

theorem BirkhoffGlobalSection.convex_model_symplectic_contact_frame_pairing :
∀ {μ c : ℝ}
    (M : ConvexRegularizationModel μ c) (u : Phase) (hu : u ∈ unitThreeSphere),
    let f : Phase → ℝ := fun x => ((gauge M.body x)⁻¹)^2
    let A := convexModelSymplecticContactFrame M u 0
    let B := convexModelSymplecticContactFrame M u 1
    fderiv ℝ (fun x => f x * phaseRadialContact x B) u A -
      fderiv ℝ (fun x => f x * phaseRadialContact x A) u B = 1 := by sorry

Source

Independent extraction of component 13 of the Proved theorem BirkhoffGlobalSection.contact_frame_basis_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_contact_frame_basis_bundle.lean. Exact original component retained.

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