Convex model contact variation path initial
ProvedBirkhoffGlobalSection.convex_model_contact_variation_path_initialconvex-geometryreal-analysis
With sphere initial base point and identity initial variational matrix, the convex model contact-coordinate action equals the identity at time zero.
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_variation_preservation_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_variation_path_initial :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (q : ℝ → Phase)
(Z : ℝ → (Phase →L[ℝ] Phase)) (hs : q 0 ∈ unitThreeSphere)
(hZ0 : Z 0 = ContinuousLinearMap.id ℝ Phase) (p : Plane),
convexModelContactVariationPath M q Z 0 p = p := by sorrySource
Independent extraction of component 9 of the Proved theorem BirkhoffGlobalSection.contact_variation_preservation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_contact_variation_preservation_bundle.lean. Exact original component retained.