Courtade–Kumar proof module `CKLaneC.RSC2.BB_0067` (transplant)

Definition

CK_CKLaneC_RSC2_BB_0067

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

general-courtade-kumartransplant

Verbatim transplant of the Lean module CKLaneC.RSC2.BB_0067 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.BB_0067 from release v1.0 (sources_v3.tar.zst).

Definition code

import Definitions.Def_CK_CKLaneC_RSC2_BB_0067_part01

/-! RA-stat cover batch BB_0067 (generated by tools/emit_cover2.py; compact format). -/

namespace CKLaneC.RSC2.BB_0067
open CKLaneC.TM3 CKLaneC.RSCell

theorem region : RegionPosI 5764607523034234880 6917529027641081856 4611686018427387904 9223372036854775808 14411518807585587200 16429131440647569408 :=
  (RegionPosI.split_t 6917529027641081856 (RegionPosI.split_s 15420325124116578304 (RegionPosI.split_b 6341068275337658368 (RegionPosI.of_check c0 q0 ok_0 5764607523034234880 6341068275337658368 4611686018427387904 6917529027641081856 14411518807585587200 15420325124116578304 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 6341068275337658368 6917529027641081856 4611686018427387904 6917529027641081856 14411518807585587200 15420325124116578304 (by decide +kernel))) (RegionPosI.split_b 6341068275337658368 (RegionPosI.of_check c2 q2 ok_2 5764607523034234880 6341068275337658368 4611686018427387904 6917529027641081856 15420325124116578304 16429131440647569408 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 6341068275337658368 6917529027641081856 4611686018427387904 6917529027641081856 15420325124116578304 16429131440647569408 (by decide +kernel)))) (RegionPosI.split_s 15420325124116578304 (RegionPosI.split_b 6341068275337658368 (RegionPosI.of_check c4 q4 ok_4 5764607523034234880 6341068275337658368 6917529027641081856 9223372036854775808 14411518807585587200 15420325124116578304 (by decide +kernel)) (RegionPosI.of_check c5 q5 ok_5 6341068275337658368 6917529027641081856 6917529027641081856 9223372036854775808 14411518807585587200 15420325124116578304 (by decide +kernel))) (RegionPosI.split_b 6341068275337658368 (RegionPosI.of_check c6 q6 ok_6 5764607523034234880 6341068275337658368 6917529027641081856 9223372036854775808 15420325124116578304 16429131440647569408 (by decide +kernel)) (RegionPosI.of_check c7 q7 ok_7 6341068275337658368 6917529027641081856 6917529027641081856 9223372036854775808 15420325124116578304 16429131440647569408 (by decide +kernel)))))

end CKLaneC.RSC2.BB_0067

Source

arXiv:2609.24931; https://github.com/dpwoodru/general-courtade-kumar-lean release v1.0, module CKLaneC.RSC2.BB_0067 (browse copy where available: https://github.com/dpwoodru/general-courtade-kumar-lean/blob/04b6fc3f75b10c3c43702a883ddf888b0608a9a0/browse/CKLaneC/RSC2/BB_0067.lean)

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