Courtade–Kumar proof module `CKLaneC.RSC2.S02_0048` (transplant)

Definition

CK_CKLaneC_RSC2_S02_0048

by tianyipeng · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

general-courtade-kumartransplant

Verbatim transplant of the Lean module CKLaneC.RSC2.S02_0048 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 CKLaneC.RSC2.S02_0048 from release v1.0 (sources_v3.tar.zst).

Definition code

import Definitions.Def_CK_CKLaneC_RSC2_S02_0048_part02

/-! RA-stat cover batch S02_0048 (generated by tools/emit_cover2.py; compact format). -/

namespace CKLaneC.RSC2.S02_0048
open CKLaneC.TM3 CKLaneC.RSCell

theorem region : RegionPosI 2251799813685248 2814749767106560 0 4611686018427387904 4035225266123964416 4611686018427387904 :=
  (RegionPosI.split_b 2533274790395904 (RegionPosI.split_s 4323455642275676160 (RegionPosI.split_b 2392537302040576 (RegionPosI.of_check c0 q0 ok_0 2251799813685248 2392537302040576 0 4611686018427387904 4035225266123964416 4323455642275676160 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 2392537302040576 2533274790395904 0 4611686018427387904 4035225266123964416 4323455642275676160 (by decide +kernel))) (RegionPosI.split_b 2392537302040576 (RegionPosI.of_check c2 q2 ok_2 2251799813685248 2392537302040576 0 4611686018427387904 4323455642275676160 4611686018427387904 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 2392537302040576 2533274790395904 0 4611686018427387904 4323455642275676160 4611686018427387904 (by decide +kernel)))) (RegionPosI.split_s 4323455642275676160 (RegionPosI.split_b 2674012278751232 (RegionPosI.of_check c4 q4 ok_4 2533274790395904 2674012278751232 0 4611686018427387904 4035225266123964416 4323455642275676160 (by decide +kernel)) (RegionPosI.of_check c5 q5 ok_5 2674012278751232 2814749767106560 0 4611686018427387904 4035225266123964416 4323455642275676160 (by decide +kernel))) (RegionPosI.split_b 2674012278751232 (RegionPosI.of_check c6 q6 ok_6 2533274790395904 2674012278751232 0 4611686018427387904 4323455642275676160 4611686018427387904 (by decide +kernel)) (RegionPosI.of_check c7 q7 ok_7 2674012278751232 2814749767106560 0 4611686018427387904 4323455642275676160 4611686018427387904 (by decide +kernel)))))

end CKLaneC.RSC2.S02_0048

Source

arXiv:2609.24931; https://github.com/dpwoodru/general-courtade-kumar-lean release v1.0, module CKLaneC.RSC2.S02_0048 (browse copy where available: https://github.com/dpwoodru/general-courtade-kumar-lean/blob/04b6fc3f75b10c3c43702a883ddf888b0608a9a0/browse/CKLaneC/RSC2/S02_0048.lean)

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