Round-six lemma `g32_ok`

Proved

R6Chk.Bit.DagC.g32_ok

by xuanji · Oct 20, 2026 · Mathlib 0df444a (Lean v4.33.1)

complexity-theoryinteger-multiplicationkappa-improvement

An auxiliary lemma of the round-six development, published as a separate node because its proof is long or shared.

The following holds (Lean statement, in the scope of module Solutions.R6ChkBitDagC):

theorem R6Chk.Bit.DagC.g32_ok : allL (gchunkChk supG) g32 = true

Context. Bit round six, h = 23: kernel checks of the gm-side DAG against the support table. 174 gate chunks (200 gates each), 27 output chunks, 1 retained chunk. Generated by bit_dagmod.py.

Formalization Note. Part of the Lean formalization of the round-six κ-improvement (integer-multiplication-kappa campaign, target IntMul.Kappa.jain_round6_framework). The statement is copied verbatim from the Lean development; the platform node carries the same declaration name. Definitions it mentions live in the IntMul_Kappa_R6_Defs* bundles (on top of the published κ bundles IntMul_Kappa_K_Defs*).

Preamble

-- Round-six κ development (integer-multiplication-kappa), generated by skeleton subtraction.

import Definitions.Def_IntMul_Kappa_R6_Defs51

set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 1000000

open R6Chk R6Chk.Bit R6Chk.Bit.DagC
open R6Chk R6Chk.Bit

Formal statement

theorem R6Chk.Bit.DagC.g32_ok : allL (gchunkChk supG) g32 = true := by sorry

Source

S. Jain, round-six networks for the integer-multiplication κ-improvement campaign (https://github.com/Swapnil-jain/integer-mult-kappa, commit 5868dc7) and D. Colkitt, integer-mult-bounds (https://github.com/CrocSwap/integer-mult-bounds); target `IntMul.Kappa.jain_round6_framework`. Lean declaration `R6Chk.Bit.DagC.g32_ok`, Solutions/R6ChkBitDagC.lean (lines 274–274) of the round-six development.

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