Pith Number

pith:CJVUMNS2

pith:2012:CJVUMNS2WQXGZXY2P5SAPVI4JP

not attested not anchored not stored refs pending

A Structure Theorem for Small Sumsets in Nonabelian Groups

Gilles Z\'emor, Oriol Serra

arxiv:1203.0654 v1 · 2012-03-03 · math.CO · 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{CJVUMNS2WQXGZXY2P5SAPVI4JP}

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	2026-05-18T03:11:24.191766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

126b46365ab42e6cdf1a7f6407d51c4bc71d2cb3603f6dacba61d51ffe4c5585

Aliases

arxiv: 1203.0654 · arxiv_version: 1203.0654v1 · doi: 10.48550/arxiv.1203.0654 · pith_short_12: CJVUMNS2WQXG · pith_short_16: CJVUMNS2WQXGZXY2 · pith_short_8: CJVUMNS2

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/CJVUMNS2WQXGZXY2P5SAPVI4JP \
  | 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: 126b46365ab42e6cdf1a7f6407d51c4bc71d2cb3603f6dacba61d51ffe4c5585

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49bad29f409834ef238113561505234e667ace349ade3b9ac2be464811ec2799",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-03T13:52:34Z",
    "title_canon_sha256": "5e443b2cf1358661e3df758d59df96e532a548186331bec38bb054d933f4ecbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0654",
    "kind": "arxiv",
    "version": 1
  }
}