Pith Number

pith:QU4E55KL

pith:2024:QU4E55KLU3BZPIEXUSGTUG5WED

not attested not anchored not stored refs pending

Dissecting Multiplication in Transformers: Insights into LLMs

Chen Jason Zhang, Chi Su, Jianing Li, Lei Chen, Luyu Qiu

arxiv:2407.15360 v1 · 2024-07-22 · cs.CL

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\usepackage{pith}
\pithnumber{QU4E55KLU3BZPIEXUSGTUG5WED}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

2 papers in Pith

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models

On the Mirage of Long-Range Dependency, with an Application to Integer Multiplication

Receipt and verification

First computed	2026-07-05T08:46:42.682547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85384ef54ba6c397a097a48d3a1bb620e6f3c357b3414a9ca0f8bff9d31a86e8

Aliases

arxiv: 2407.15360 · arxiv_version: 2407.15360v1 · doi: 10.48550/arxiv.2407.15360 · pith_short_12: QU4E55KLU3BZ · pith_short_16: QU4E55KLU3BZPIEX · pith_short_8: QU4E55KL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QU4E55KLU3BZPIEXUSGTUG5WED \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 85384ef54ba6c397a097a48d3a1bb620e6f3c357b3414a9ca0f8bff9d31a86e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0811ac1ed46f33ccf12fd3452cf072e63b63b81e6b7921d5a30fde49d78d9f96",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2024-07-22T04:07:26Z",
    "title_canon_sha256": "c07441c48cbe3453a6f935e58cb043d81a3b9c5f95b90c9bcb7f0bb339483b40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.15360",
    "kind": "arxiv",
    "version": 1
  }
}