R8 BitNB GenData seed SG1_0 (NL=31359 initial labels)

Definition
IntMul_Kappa_R8_Data_BitOppbankGenData_0
by Ethan Cheung Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)
bitnbgendataintmulkapparound8
GenData seed: initial stage-1 labels

Round-six BitNB stores stage words as packed maps $\mathrm{wire}\mapsto\mathrm{code}$ (codeOf). The initial stage-1 state SG1_0 before genF sets $\mathrm{code}(w_X(x))=c_{ND}(x+1)$ on the length- $v$ entrance block and $0$ elsewhere (cf. init1 in IntMul_Kappa_R6_Defs51).
This module emits that seed for the R8 local-wire count $N_L=31359$ ( $NR=27794$ ). Later SG* snapshots need genF over an R7-retargeted Loc pack (GREC/RETS/INJ still reference slots up to $40076$ in R6 data).
Definition code
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Nat.Bitwise

set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 8000000
set_option maxRecDepth 100000

/-!
# R8 BitNB GenData seed — initial stage-1 label pack `SG1_0`

For local-wire count `NL = 31359` (`= 2v + NR + h` with `NR = 27794`), the R6
`init1`/`SG1_0` seed pattern on the `wX` block is geometry-only:

* `code(wX x) = cND(x+1) = 1774+x` for `x < v = 1771`
* all other wires `0` pending R7 Loc (`retN` for `wT`, slot labels from `genF`)

Packed as 16-bit fields LSB-first in 65536-bit `packL` limbs (R6 GenData convention).
Full `SG1_1..` / `SG2_*` require running `Defs51.genF` on an R7-retargeted Loc
(`GREC`/`INJ`/`RETS` currently max out at slot `40076`).
-/

namespace IntMul.Kappa.R8.Bit.Oppbank.Gen

def packL (l : List Nat) : Nat :=
  l.foldr (fun p acc => Nat.lor p (Nat.shiftLeft acc 65536)) 0

def NL : ℕ := 31359

/-- Initial stage-1 label state (`NL` wires). -/
def SG1_0 : Nat :=
  packL [
  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,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0,
  0x0
  ]

def field16 (S i : Nat) : Nat := (S >>> (16 * i)) &&& 65535
def codeOf (S : Nat) (w : Nat) : Nat := field16 S w

end IntMul.Kappa.R8.Bit.Oppbank.Gen
Source
Pattern from Prove2me IntMul_Kappa_R6_Defs51 init1 / BitNBGenData SG1_0; geometry IntMul_Kappa_R8_Data_BitOppbankConsts (NL=31359).
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