Pith Number

pith:3CD62Z3X

pith:2010:3CD62Z3XRXBP3ZM7UZUERWW54F

not attested not anchored not stored refs pending

String numbers of abelian groups

Anna Giordano Bruno, Simone Virili

arxiv:1006.5206 v3 · 2010-06-27 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3CD62Z3XRXBP3ZM7UZUERWW54F}

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	2026-05-18T04:33:07.285267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d887ed67778dc2fde59fa66848dadde170e96f29b10eb42a189ad6317810bfe8

Aliases

arxiv: 1006.5206 · arxiv_version: 1006.5206v3 · doi: 10.48550/arxiv.1006.5206 · pith_short_12: 3CD62Z3XRXBP · pith_short_16: 3CD62Z3XRXBP3ZM7 · pith_short_8: 3CD62Z3X

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/3CD62Z3XRXBP3ZM7UZUERWW54F \
  | 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: d887ed67778dc2fde59fa66848dadde170e96f29b10eb42a189ad6317810bfe8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "632d701a567ab33a8fe19d6626616dbaf4d192b8372207d4266db798fc398d42",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-27T12:52:27Z",
    "title_canon_sha256": "e70bc754d6e72b818507264aad0c71f195daf6ef1e9d59a4f4e9a5432ddc6b93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5206",
    "kind": "arxiv",
    "version": 3
  }
}