R8 opp-bank Loc GREC producer records

Definition
IntMul_Kappa_R8_Data_BitOppbankLocGrec
by Ethan Cheung Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)
bitnbinteger-multiplicationkappaoppbankr8
Producer-record table $\mathrm{GREC}$ for the round-eight bit network at $R=27794$ .
Each chunk packs up to 256 records $(n,\mathrm{pivot},\mathrm{other}+1,\mathrm{extras})$ in the R6 BitNB layout. One record is emitted per jfstack hold/opreg node (54290), in DAG topo order; complex lifted opreg words are abstracted to this Rec shape via first slot appearance.
Role: feeds mixF/mixI in the stage words that genF runs to produce SG* code states.
Formalization Note. Namespace IntMul.Kappa.R8.Bit.Oppbank.LocGrec; source Jain jfstack_23.json.gz.
Definition code
import Mathlib.Data.Nat.Basic

set_option autoImplicit false
set_option relaxedAutoImplicit false

/-!
# R8 opp-bank Loc GREC (producer records) from Jain jfstack_23

Auto-emitted by emit_grec_full.py. One `Rec` per schedule node in `hold`/`opreg`
(54290), topo-ordered by DAG args. Complex opreg linear words are abstracted to
R6-shaped `(n, pivot, other+1, extras)` using first slot appearance in `hold`.

Source: `certificates/round7/jfstack_23.json.gz` via `jfdata.load(23)`.
-/

namespace IntMul.Kappa.R8.Bit.Oppbank.LocGrec

/-- Producer records (≤256 per chunk): n(16), pivot(16), second+1(16), ne(8), extras. -/
def GREC : List ℕ := [
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]

def GREC_len : ℕ := 213
theorem GREC_len_eq : GREC_len = 213 := rfl

end IntMul.Kappa.R8.Bit.Oppbank.LocGrec
Source
Jain integer-mult-kappa certificates/round7/jfstack_23.json.gz; R6 BitNB Defs51 genF/GREC layout from Prove2me IntMul_Kappa_R6_Data_BitNB*.
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