R8 opp-bank aux-slot retained dimensions f[s] (packed)

Definition
IntMul_Kappa_R8_Data_BitOppbankAuxF
by Ethan Cheung Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)
bitnbintmulkappaoppbankround8schedule
Opp-bank aux-slot retained dimensions

For Jain's round-seven witness 2 joint-frame schedule, each aux slot $s<R=27794$ carries a retained-frame dimension $f[s]\in\{0,\ldots,22\}$ . The round-eight opposite-bank compile treats the aux edge at slot $s$ as a single child of width $m-(h-f[s])$ with $h=23$ and $m=529$ (see independent/round8-oppbank/bit_hist.py).
This module packs the frozen list $f[\cdot]$ as 8-bit fields in 65536-bit packL limbs (R6 BitNB convention) and exposes auxF / auxCorner. It is schedule data, not a QHNet Gen/Loc pack.
Definition code
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Nat.Bitwise

set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 4000000
set_option maxRecDepth 100000

/-!
# R8 opp-bank aux-slot retained dimensions `f[s]` (packed)

Frozen joint-frame schedule from Jain `certificate_round7` witness 2 (`S.f`),
length `R = 27794`, values in `0..22`. Packed as 8-bit fields LSB-first in
65536-bit limbs (`packL`), matching the R6 BitNB packing discipline.

Opp-bank aux-edge corner width is `h - f[s]` with `h = 23`. Schedule data only.
-/

namespace IntMul.Kappa.R8.Bit.Oppbank

/-- Concatenate 65536-bit pieces, least significant first (R6 `BitNBGenData` convention). -/
def packL (l : List Nat) : Nat :=
  l.foldr (fun p acc => Nat.lor p (Nat.shiftLeft acc 65536)) 0

/-- Packed retained dimensions: field `s` (8 bits) is `f[s]` for `s < 27794`. -/
def auxFPack : Nat :=
  packL [
  0x1600150000000016001500001614000013000016150000130000160014000000001614000013000016150013000016150013000016150000130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000014000016150000140000160015000000001614000014000016150013000016150013000016150000140000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000000000000000000000000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000161400001300001615000013000016001400000000161400001300001615001300001615001300001615000013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001400001615000014000016001500000000161400001400001615001300001615001300001615000014000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000000000000000000000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500001614000013000016150000130000160014000000001614000013000016150013000016150013000016150000130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000014000016150000140000160015000000001614000014000016150013000016150013000016150000140000161500130000161500130000160015000001001614000014000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000000005000000000000000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000040016001500000000160015000000001600150000000016001500000000160015000000001600150000040016001500000000160015000000001600150000000016001500001614000013000016150000130000160014000000001614000013000016150013000016150013000016150000130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000003001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000003001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160014000000001614000014000016150000140000160015000000001614000014000016150013000016150013000016150000140000161500130000161500130000160015000003001614000014000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000001614000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000160015000000000003000000000000000000160015000003001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000040016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000,
  0x100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000010100000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010100000100000000000000000000000000000000000000000000000000000000010100000000000000000000000000000000000000000000000000000000000000000000000000010000010000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000200010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010100000100000000000000000000000000000000000000000000000000000000010100000000000000000000000000000000000000000000000000000000000000000000000000010000010000000000000000000000000000000000000000000000000000000000000000000000000000010000010000000000000000000000000000000000000000000100000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000161400001300001615000013000016001400000000161400001400001615000014000016001500000000000400000000000000000016001500000400160015000016140000130000161500001300001600140000000016140000130000161500130000161500130000161500001300001615001300001615001300001600140000000016140000140000161500001400001600150000000016140000140000161500130000161500130000161500001400001615001300001615001300001600150000040000060000000000000000001600150000040016001500000000160015000004001600150000161400001300001615000013000016001400000000161400001300001615001300001615001300001615000013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016001400000000161400001400001615000014000016001500000000161400001400001615001300001615001300001615000014000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016001500000000000000000000000000000016001500000000160015000000001600150000000016001500000000160015000003001600150000161400001300001615000013000016001400000000161400001300001615001300001615001300001615000013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001400001615000014000016001500000300161400001400001615001300001615001300001615000014000016150013000016150013000016001500000400161400001400001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016001500000300000000000000000000000016001500000000160015000000001600150000000016001500000000160015000003001600150000000016001500000300160015000016140000130000161500001300001600140000030016140000130000161500130000161500130000161500001300001615001300001615001300001600140000000016140000130000161500130000161500130000161500130000161500130000161500001300001615001300001615001300001615001300001615001300001600140000000016140000130000161500130000161500130000161500130000161500130000161500130000161500130000161500001300001615001300001615001300001615001300001615001300001615001300001615001300001600140000000016140000130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001600140000000016140000140000161500001400001600150000000016140000140000161500130000161500130000161500001400001615001300001615001300001600150000000016140000140000161500130000161500130000161500130000161500130000161500001400001615001300001615001300001615001300001615001300001600150000000016140000140000161500130000161500130000161500130000161500130000161500130000161500130000161500001400001615001300001615001300001615001300001615001300001615001300001615001300001600150000030016140000140000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500130000161500001400001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001600150000000000000000000000000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000000016001500000000160015000000001600150000161400001300001615000013000016001400000000161400001300001615001300001615001300001615000013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001400000000161400001400001615000014000016001500000000161400001400001615001300001615001300001615000014000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000161400001400001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615001300001615000014000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016150013000016001500000000000000000000000000000016001500000000160015000000001600150000000016001500000000160015000003001600150000000016001500000000160015000000001600150000000016001500000000,
  0x121212121212121212121212121212121111141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131312121312131212131212131212131212131212131212131313121313121313131313131313131212121112121212121212121212121212121212121212121212121212131313141414131313141414131313141414131313141414141414141414141414141414131313141414131313141414141414141414141414141414141414141414141414141414131313141414131313141414141414141414141414141414141414141414141414141414141414141414141414141414131312141212141212141212141212141212141212141212141212141313131313131313131314141414141414141214121212121212121212121212121212121212121212121212121112111414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141313131313131414141414141313131313131414141414141313131313131414141414141313131313131212131213121213121213121213121213121213121213121213131312131313131313131313131212121212121212121212121212121212121212121212121212121212121414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131414131212141214121214121214121214121214121214121214121214121214131313131313131313131414141414141414141412121212121212121212121212121212121212121212121212121212121214141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141412121312131212131212131212131212131212131212131212131212130f0f10100f0f10100f0f101010110d0d001014100d0d0000001100110d0d101014001400100000001013001210120d0d10101400140014001000000010131013001210120f0f1010140014001400141010101010101310130013001210120d0f101014001400140014101410101000001013101310131013001210120f0f00101400140014001400141014101010100010131013001310131013001210120f0f1010140014001400140014101410141010101010101310131013101310131013001210120f0f101014001400140014001410140014101410101010101013101310131013101310131013001210120d0f1010140014001400140c1410141014101410141010101010001300130013101310131013101310131012101210101010130013001300131013101310131013101310131010101010000d0b0b0b0b0b0b0b0c0b0b0c0d000b0d000c000c0b0c0c100c100b000809070805070807070d0c0c0a08050a080e0e0a000d10060d0c0c0d0c0c0d0c0c0e0b0b040809080608080808081008000f0909080c050b0c07070d0c0c0d0c050c0c0e0e0e0d0d0e0710000d0c0c0d0a0c0d05080e0b0b0d0c050c070d0d0d0a0c0e0c0c0f0c0f0506030702060906070d0c0c0e0705090d090e0e0e0d0d0d03110000000d0c0c0d0a0c0906080e0b0c0407050703080b0c06040f0d0a110c100c100905030901030d05070a0a070e000d000d000c000c080a10071100000010000d0c0c090a0807040400090700000500070c000c08080f0d0a1006110a100a10090a0a0d080c070a050c07070000030009000a0006000c000f0911000000110011000d0c0c000c090806030007070707000e000c0b080d0a10090d0c110a1108110c100a100907070d080c0d070c0c09090e000d0d0a000e0d0a0c000c0f0911000000110011001000000d070d0d0b0906060009090a000d0d090c0b090d0c0f00100a00100a110a1106110c100a100d0c0c0b08070808010c08050a00050d09000c090c0c000c1000110000001100110a110011000b0a0a0d0a0b0908050007050b0005000a0c0b060c000f0d0f0c0d00110a110c110a11061108100a100d0b0c0b08080708030c08070b000d000a000d0c000c000c0f0d1011000000110c110a1100110010000a070500040309080b0c07070e0005000d0a0c040a0d10000f0c0d0c100c110c110c110c1108110c100c100d0b0b0d070b0d0b070c0c0b0d0609070a03080a0c0804070f0d100a10000e0010001000100a100c10000f000a060407040609060c0e0b0b0e0905090d0c0d080c0d0c10060c0d0c0c110c1100110c1100110c110011001000100d0b0b0d0b0b09070b0c0b0b090c080c080c0a000a0a080a0e0b0e001100110011001100110a11001100100011000009070007070a07070c0b0b0d0c0c0c0b0c0e080c0d0c0e080c0d0c001000110c110c110c1100110c1100110c1000100c0b0b0c090b0807070c0c0b080a080a060a0c000c0c080c100800000c11001100110c1108110a110011001000110010000a0b0700090b0906070c0b0b080a080c080a0c0c0c0c0c0c10060c0c0c070b0e0c050b070b0f000d00040c040c030b0c000d000e0c020c020c010c0c0b0f000d000b0c0f0c0c0f040002000600050c0c000a0005080c080b08080b080c020b020b050b0c0b0f000d000b0a0f0a0f080f0c0c0f080f0a0f040a040a0800070c00000c000a0400080b0600060d080c0e0c0f08090a0f080a04000800070c00000000000400040b0200020d020d080b0c0c0d0c0d070d080d070c04000700080a00000f0000080008000500060d010d040005000c000c0b0c0b0c080f070c0c080c08080a0c0c0f000f000f080f080f0c0f050f0c000c000c0c0700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a080a080507070a0a000a0004080307030a060006000608040a020801070208040008000308070a080d040c020c0508040806000b000608070a090a0a090a0d040c040b070c080708000a000608060a0c0a0b080a0d0a0d0a0d0a0c040c0704080608000d0006020d040d0a0c0a0d0a0809080308060803060302060502080108000a0008020a020b0209080d020908080808040706070408060705040a0705080608000d000505090509050b030d03090308070008000808060804080608060606020a050606050d000d00040a08060806080608040c0a080a080a0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000500000000000500000000000700000003070000050000000308000005000000010703070000050000000300010000000500000002080008000700000500000001000000020800000300000002080008000700070000050000000000000000080208000001000000080000080208040803070000000000000300030002080008000800000000000000000808040806080408030700000100000003000300020800080000080800000500000008020800080002020202050004000000030000000300050002000202000008080808000007000000080208000000080202020002040203010000050000000300030000020202000008060800080600000500000007010800070000000804030302040503030300000500000003000500020400030000080407000800070100000700000000030003070008000000070306060103080303030000070000000300050001030006000007030800070008030703000005000000000000000300000000000000000000060000000000000404000000000001000300000000000003000100000000000004000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000600000003000400000000000000000000000000000006000000000000000000000004000100010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006000000000000000000000000000000000000000000000000000000000000000000000000000000000004000000000000000300000000000000000000000100020000000000000000000000000000000000000000000000000000000000000000000000040000000000000000000100010000000000000000000000000000000000040004000000010006000000000000000000000000010000010000010001010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300000300000300000300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000030000030000030300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000300000300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003000003000000030000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010000000000010000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000301000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010001030001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000001000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300030003000003000003000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300000100000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003000000000300000300000300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001010000010000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300030000000000030000030000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000103000001000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300030003000003000000030003030000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300010000000100000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000030003000300000300000003000003000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010001000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000100010002000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000001010000010000000000000000000000000000000000000000000000000100000000000000000000000000000001000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000100000000000000000000000000000000000000000000010000000000000000000000000100000100000000000000000000000000000000000000000000000000010000000000000000000000000000010000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,
  0x1314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131314131413141413141413141413141413141413141413141413141413141413141212121212121212121212121212121212121112131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131213121313121313121313121313121313121313121313121313121313131313131313131312121212121212121212111112121212121212121313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131213121313121313121313121313121313121313121313121313121212121212121212131212121212121212121212111213131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131213121313121313121313121313121313121313121313121212141313131313131313131312121212121212121214121112111212121212121212131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131312121313121313121313121313121313121313121313121313121313121212121212121213131212121212121211121212121212121313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313121312131312131312131312131312131312131312121214121214131313131313131313131412121212121212121412121212121211111212121212121313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131212131213131312131312131312131312131312131312131312131312121212121212131313121212121212121212111212121212121213131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131414141313131414131312131213131213131213131213131213131212121412121412121413131313131313131313141412121212121212141212121212121211121112121212121214141414141413131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313121213121312121313131213131213131213131213131213131213131212121212121313131312121212121112121212121212121212121212131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131314141414141414141414141313121312131312131312131312131312121214121214121214121214131313131313131313131414141212121212121412121212121212121212121211111212121214141414141414141414141413131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313121213121312121312121313131213131213131213131213131213131212121212131313131312121212121212111212121212121212121212121213131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131314141413131314141413131313131313131313131313131313131313131313131313131414141313131414141414141414141414141414131312131213131213131213131212121412121412121412121412121413131313131313131313141414141212121212141212121212121212121212121211121112121212141414141414141414141414141414141414131313131313141414141414131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131212131213121213121213121213131312131312131312131312131312121212131313131313121212111212121212121212121212121212121212121213131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131314141414141414141414141413131313131313131313131313131313131313131313131414141414141414141414141414141414141414141414141313121312131312131312121214121214121214121214121214121214131313131313131313131414141414121212121412121212121212121212121212121212121211111212141414141414141414141414141414141414141414141414141414141414141414141414131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131212131213121213121213121213121213131312131312131312131312121213131313131313121212121211121212121212121212121212121212121212121313131313131313131313131313131313131313131313131313131414141313131414141313131313131313131313131313131414141313131414141414141414141414141414141313131313131313131313131313141414131313141414141414141414141414141414141414141414141414141414131312131213131212121412121412121412121412121412121412121413131313131313131313141414141414121212141212121212121212121212121212121212121211121112121414141414141414141414141414141414141414141414141414141414141414141414141414141414141313131313131414141414141313131313131414141414141313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313121213131212131212131212131212131212131313121313121313121213131313131313131211121212121212121212121212121212121212121212121212121313131313131313131313131313131313131313131313131414141414141414141414141313131313131313131313131414141414141414141414141414141414141414141414141313131313131313131313141414141414141414141414141414141414141414141414141414141414141414141414131312131212121412121412121412121412121412121412121412121413131313131313131313141414141414141212141212121212121212
  ]

/-- Read 8-bit field `i` of a packed `Nat`. -/
def field8 (S i : Nat) : Nat :=
  (S >>> (8 * i)) &&& 255

/-- Retained dimension `f[s]` (returns `0` for out-of-range `s`). -/
def auxF (s : Nat) : Nat := field8 auxFPack s

/-- Corner rank `r_u(s) = 23 - f[s]`. -/
def auxCorner (s : Nat) : Nat := 23 - auxF s

end IntMul.Kappa.R8.Bit.Oppbank
Source
Swapnil Jain, integer-mult-kappa certificates/round7 witness 2 via certificate_round7.build (S.f); packing discipline as Prove2me IntMul_Kappa_R6_Data_BitNBGenData_*.
View graph