Convex model radial right inverse tangent
ProvedBirkhoffGlobalSection.convex_model_radial_right_inverse_tangentconvex-geometryreal-analysis
On energy-tangent boundary vectors, the convex model gauge-chart derivative is a right inverse of the radial-normalization derivative.
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_reverse_radial_variation_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_radial_right_inverse_tangent :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (y w : Phase) (hy : y ∈ frontier M.body)
(hw : fderiv ℝ M.modelHamiltonian y w = 0),
fderiv ℝ (fun x : Phase => (gauge M.body x)⁻¹ • x) (radialNormalize y)
(fderiv ℝ radialNormalize y w) = w := by sorrySource
Independent extraction of component 8 of the Proved theorem BirkhoffGlobalSection.reverse_radial_variation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_reverse_radial_variation_bundle.lean. Exact original component retained.