Pith Number

pith:V2CZZDND

pith:2010:V2CZZDND7ZYBI7HLRRRRKJFSNB

not attested not anchored not stored refs pending

Galois Representations with Quaternion Multiplications Associated to Noncongruence Modular Forms

A.O.L. Atkin, Ling Long, Tong Liu, Wen-Ching Winnie Li

arxiv:1005.4105 v4 · 2010-05-22 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V2CZZDND7ZYBI7HLRRRRKJFSNB}

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.

Receipt and verification

First computed	2026-05-18T04:14:38.223165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae859c8da3fe70147ceb8c631524b2684f32a9489c4bcb9b199dbd783a2159d5

Aliases

arxiv: 1005.4105 · arxiv_version: 1005.4105v4 · doi: 10.48550/arxiv.1005.4105 · pith_short_12: V2CZZDND7ZYB · pith_short_16: V2CZZDND7ZYBI7HL · pith_short_8: V2CZZDND

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/V2CZZDND7ZYBI7HLRRRRKJFSNB \
  | 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: ae859c8da3fe70147ceb8c631524b2684f32a9489c4bcb9b199dbd783a2159d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b9f63cbc3df3217cd54f0a0d0cd78381a60c2f2e595dbb41ce6caa7d1017dfa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-05-22T05:49:06Z",
    "title_canon_sha256": "a65951cadb16bd85def6e2e4cb3724226afe0c8618c510c8e641b3e3357a9bfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.4105",
    "kind": "arxiv",
    "version": 4
  }
}