Round-six network data, CxNetDataS2_13m
DefinitionIntMul_Kappa_R6_Data_CxNetDataS2_13mcomplexity-theoryinteger-multiplicationkappa-improvement
Data bundle IntMul_Kappa_R6_Data_CxNetDataS2_13m of the round-six κ-improvement development: literal network data from the Lean module R6Pk.R6CxNetDataS2_13m (S2_13m: the code state halfway through segment 13 of stage 2; H2_13a, H2_13b: packed move histograms of the two halves of that segment), stored as Lean terms (large natural-number literals, BT trees and lists of numbers). These values are not proved correct by themselves; they are the certificates and snapshots that the kernel checks (decide +kernel nodes) evaluate. A value larger than one bundle is split into parts (X_p…) that are reassembled by an exact node/++ expression, so the reassembled term is definitionally the original one.
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*).
Definition code
-- Round-six κ development (integer-multiplication-kappa), generated by skeleton subtraction.
import Definitions.Def_IntMul_Kappa_R6_Defs24
set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 1000000
set_option maxRecDepth 100000
namespace IntMul.Kappa.R6.Cx.NetData
open NetBT
/-- Code state snapshot of stage 2 inside segment 13: after the readout wires and the first 24604 scratch wires. -/
def S2_13m : BT :=
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/-- Packed histogram of the first half of segment 13 of stage 2 (`{23: 2024, 1: 14696, 2: 4184, 5: 1421, 6: 702, 4: 210, 8: 614, 10: 352, 12: 212, 16: 366, 20: 212, 14: 264, 18: 352, 22: 11, 7: 284, 9: 128, 13: 96, 11: 104, 15: 104, 17: 192, 19: 100}`). -/
def H2_13a : ℕ := 0x7e80000b00000000d40006400160000c00016e000680010800060000d4000680016000080002660011c002be0058d000d200000010580396800000
/-- Packed histogram of the second half of segment 13 of stage 2 (`{5: 1899, 7: 1420, 9: 640, 13: 480, 11: 520, 15: 518, 17: 959, 19: 1700, 2: 4000, 4: 552, 6: 552, 8: 552, 10: 552, 12: 552, 14: 552, 16: 552, 18: 3808, 20: 4796}`). -/
def H2_13b : ℕ := 0x12bc006a400ee0003bf002280020600228001e000228002080022800280002280058c002280076b002280000000fa00000000000
end IntMul.Kappa.R6.Cx.NetData
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 module R6Pk/R6CxNetDataS2_13m.lean (generated data, computed by replaying the stage-2 program to the middle of segment 13).