Courtade–Kumar proof module `CKLaneC.RSC2.S02_0164` (transplant)

Definition

CK_CKLaneC_RSC2_S02_0164

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

general-courtade-kumartransplant

Verbatim transplant of the Lean module CKLaneC.RSC2.S02_0164 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_0164 from release v1.0 (sources_v3.tar.zst).

Definition code

import Definitions.Def_CK_CKLaneC_RSC2_S02_0164_part02

/-! RA-stat cover batch S02_0164 (generated by tools/emit_cover2.py; compact format). -/

namespace CKLaneC.RSC2.S02_0164
open CKLaneC.TM3 CKLaneC.RSCell

theorem region : RegionPosI 3377699720527872 3940649673949184 13835058055282163712 18446744073709551616 8070450532247928832 9223372036854775808 :=
  (RegionPosI.split_b 3659174697238528 (RegionPosI.split_s 8646911284551352320 (RegionPosI.split_b 3518437208883200 (RegionPosI.of_check c0 q0 ok_0 3377699720527872 3518437208883200 13835058055282163712 18446744073709551616 8070450532247928832 8646911284551352320 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 3518437208883200 3659174697238528 13835058055282163712 18446744073709551616 8070450532247928832 8646911284551352320 (by decide +kernel))) (RegionPosI.split_b 3518437208883200 (RegionPosI.of_check c2 q2 ok_2 3377699720527872 3518437208883200 13835058055282163712 18446744073709551616 8646911284551352320 9223372036854775808 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 3518437208883200 3659174697238528 13835058055282163712 18446744073709551616 8646911284551352320 9223372036854775808 (by decide +kernel)))) (RegionPosI.split_s 8646911284551352320 (RegionPosI.split_b 3799912185593856 (RegionPosI.of_check c4 q4 ok_4 3659174697238528 3799912185593856 13835058055282163712 18446744073709551616 8070450532247928832 8646911284551352320 (by decide +kernel)) (RegionPosI.of_check c5 q5 ok_5 3799912185593856 3940649673949184 13835058055282163712 18446744073709551616 8070450532247928832 8646911284551352320 (by decide +kernel))) (RegionPosI.split_b 3799912185593856 (RegionPosI.of_check c6 q6 ok_6 3659174697238528 3799912185593856 13835058055282163712 18446744073709551616 8646911284551352320 9223372036854775808 (by decide +kernel)) (RegionPosI.of_check c7 q7 ok_7 3799912185593856 3940649673949184 13835058055282163712 18446744073709551616 8646911284551352320 9223372036854775808 (by decide +kernel)))))

end CKLaneC.RSC2.S02_0164

Source

arXiv:2609.24931; https://github.com/dpwoodru/general-courtade-kumar-lean release v1.0, module CKLaneC.RSC2.S02_0164 (browse copy where available: https://github.com/dpwoodru/general-courtade-kumar-lean/blob/04b6fc3f75b10c3c43702a883ddf888b0608a9a0/browse/CKLaneC/RSC2/S02_0164.lean)

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