Convex model contact coordinates linear

Proved

BirkhoffGlobalSection.convex_model_contact_coordinates_linear

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

convex-geometryreal-analysis

For a fixed convex model sphere point, contact coordinates preserve arbitrary real linear combinations of phase vectors.

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_angle_disk_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_contact_coordinates_linear :
∀ {μ c : ℝ}
    (M : ConvexRegularizationModel μ c) (u v w : Phase) (a b : ℝ),
    convexModelContactCoordinates M u (a • v + b • w) =
      a • convexModelContactCoordinates M u v + b • convexModelContactCoordinates M u w := by sorry

Source

Independent extraction of component 1 of the Proved theorem BirkhoffGlobalSection.contact_frame_angle_disk_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_contact_frame_angle_disk_bundle.lean. Exact original component retained.

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