Convex model gauge chart mem frontier
ProvedBirkhoffGlobalSection.convex_model_gauge_chart_mem_frontierconvex-geometryreal-analysis
The inverse-gauge radial chart sends every nonzero phase point to the convex model boundary.
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_gauge_chart_mem_frontier :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (u : Phase) (hu : u ≠ 0),
(gauge M.body u)⁻¹ • u ∈ frontier M.body := by sorrySource
Independent extraction of component 4 of the Proved theorem BirkhoffGlobalSection.reverse_radial_variation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_reverse_radial_variation_bundle.lean. Exact original component retained.