Pith Number

pith:562J2F4A

pith:2023:562J2F4A3B7OQZPUAR5YVB3V6X

not attested not anchored not stored refs pending

Grokking Group Multiplication with Cosets

Dashiell Stander, Honglu Fan, Qinan Yu, Stella Biderman

arxiv:2312.06581 v2 · 2023-12-11 · cs.LG · cs.AI · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{562J2F4A3B7OQZPUAR5YVB3V6X}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

Learning the symmetric group: large from small

Spectral Edge Dynamics Reveal Functional Modes of Learning

Receipt and verification

First computed	2026-07-05T08:32:33.739115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efb49d1780d87ee865f4047b8a8775f5e2922a1479ac2678f79b65795b3f12d9

Aliases

arxiv: 2312.06581 · arxiv_version: 2312.06581v2 · doi: 10.48550/arxiv.2312.06581 · pith_short_12: 562J2F4A3B7O · pith_short_16: 562J2F4A3B7OQZPU · pith_short_8: 562J2F4A

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/562J2F4A3B7OQZPUAR5YVB3V6X \
  | 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: efb49d1780d87ee865f4047b8a8775f5e2922a1479ac2678f79b65795b3f12d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a39ae01349e8c7c88b6f75bf01dbff13b394b1af0029a579f1ebcda7d0a81a6e",
    "cross_cats_sorted": [
      "cs.AI",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-12-11T18:12:18Z",
    "title_canon_sha256": "e8ff83b563dadacc7cd73bca935bebc93b6588bb6a45c939eb6e213607f46da7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.06581",
    "kind": "arxiv",
    "version": 2
  }
}