Courtade–Kumar proof module `CKLaneC2R.ReflectionBridge` (transplant)
DefinitionCK_CKLaneC2R_ReflectionBridgeVerbatim transplant of the Lean module CKLaneC2R.ReflectionBridge of the machine-checked proof of the general Courtade–Kumar theorem (the most informative Boolean function conjecture), so that the complete proof can be verified on this platform.
It is the original source with only two mechanical changes. Imports of project modules are redirected to their transplanted bundles Definitions.Def_CK_*. Declarations that already exist in earlier platform definition bundles of this mission are removed, and those bundles are imported instead, so every constant keeps a single platform identity.
The module contains both definitions and the lemmas proved alongside them in the source. They are kept together so the transplant stays faithful and every proof is re-checked by the server.
Source: Z. Chen, A. Gohari, A. Javanmard, H. Lin, V. Mirrokni, C. Nair, D. P. Woodruff, A Proof of the Most Informative Boolean Function Conjecture, arXiv:2609.24931 (2026). Lean development: https://github.com/dpwoodru/general-courtade-kumar-lean (Apache-2.0), module CKLaneC2R.ReflectionBridge from release v1.0 (sources_v3.tar.zst).
import Definitions.Def_CK_CKLaneC2R_ReflectionBridge_q00
namespace CKLaneC2R
/-- The reflection field (`Theorem71Components.reflection` / `ProductionOwners.reflection`). -/
theorem reflection_certified :
∀ a b : ℝ, 0 < b → b < a → a < 1 → 0 ≤ GeneralCK.Reflection.curvature a b :=
reflection_of_hsmall GeneralCK.Reflection.curvature_nonneg_small_bias
end CKLaneC2R