Convex model sphere contact frame independent
ProvedBirkhoffGlobalSection.convex_model_sphere_contact_frame_independentconvex-geometryreal-analysis
At every sphere point, the two convex model contact-frame vectors are linearly independent in the stated two-vector sense.
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_transverse_contact_frame_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_sphere_contact_frame_independent :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (u : Phase) (hu : u ∈ unitThreeSphere)
(a b : ℝ) (hz : a • convexModelSphereContactFrame M u 0 +
b • convexModelSphereContactFrame M u 1 = 0),
a = 0 ∧ b = 0 := by sorrySource
Independent extraction of component 11 of the Proved theorem BirkhoffGlobalSection.transverse_contact_frame_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_transverse_contact_frame_bundle.lean. Exact original component retained.