Pith Number

pith:RDMULO3W

pith:2024:RDMULO3WWU4MBVCTHJD3NBZM5M

not attested not anchored not stored refs pending

Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

Chenyang Li, Tianyi Zhou, Yingyu Liang, Zhao Song, Zhenmei Shi

arxiv:2402.09469 v4 · 2024-02-12 · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RDMULO3WWU4MBVCTHJD3NBZM5M}

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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

FoNE: Precise Single-Token Number Embeddings via Fourier Features

Convergent Evolution: How Different Language Models Learn Similar Number Representations

Receipt and verification

First computed	2026-07-05T10:27:07.571768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88d945bb76b538c0d4533a47b6872ceb0da768f8fc23ab7378164b2d78f7de2b

Aliases

arxiv: 2402.09469 · arxiv_version: 2402.09469v4 · doi: 10.48550/arxiv.2402.09469 · pith_short_12: RDMULO3WWU4M · pith_short_16: RDMULO3WWU4MBVCT · pith_short_8: RDMULO3W

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/RDMULO3WWU4MBVCTHJD3NBZM5M \
  | 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: 88d945bb76b538c0d4533a47b6872ceb0da768f8fc23ab7378164b2d78f7de2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75c31f902fe7cb848bbf3a8c61d3cb74c2463dcef95d48de03615e1061d3aa12",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-02-12T05:52:06Z",
    "title_canon_sha256": "888ea6a5ba64ea08549ebe3837a044f4e9e0fd5d2745663df27850f4c04388aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.09469",
    "kind": "arxiv",
    "version": 4
  }
}