Pith Number

pith:HEPX2RTB

pith:2023:HEPX2RTBAKR5XLWA2SJKSAITIH

not attested not anchored not stored refs pending

Teaching Arithmetic to Small Transformers

Dimitris Papailiopoulos, Jason D. Lee, Kangwook Lee, Kartik Sreenivasan, Nayoung Lee

arxiv:2307.03381 v1 · 2023-07-07 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

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\usepackage{pith}
\pithnumber{HEPX2RTBAKR5XLWA2SJKSAITIH}

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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

8 papers in Pith

Arithmetic Pedagogy for Language Models

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction

Slower Generalization, Faster Memorization: A Sweet Spot in Algorithmic Learning

FoNE: Precise Single-Token Number Embeddings via Fourier Features

LinAlg-Bench: A Forensic Benchmark Revealing Structural Failure Modes in LLM Mathematical Reasoning

Receipt and verification

First computed	2026-07-05T06:28:42.105712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

391f7d466102a3dbaec0d492a9011341d3d6661c5f25a578f41f92ee0a1a8382

Aliases

arxiv: 2307.03381 · arxiv_version: 2307.03381v1 · doi: 10.48550/arxiv.2307.03381 · pith_short_12: HEPX2RTBAKR5 · pith_short_16: HEPX2RTBAKR5XLWA · pith_short_8: HEPX2RTB

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/HEPX2RTBAKR5XLWA2SJKSAITIH \
  | 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: 391f7d466102a3dbaec0d492a9011341d3d6661c5f25a578f41f92ee0a1a8382

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "157f0e3fddd0e8980f8087741878952b42ee7ce435dbc1a2e368ce7c502bbdcb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-07-07T04:33:31Z",
    "title_canon_sha256": "88cf897613daba6cb5a94640aa5bdaadfb938ad6286bcea97f369273a66715ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.03381",
    "kind": "arxiv",
    "version": 1
  }
}