Pith Number

pith:SJ2O4RGF

pith:2010:SJ2O4RGFK2MRB2PPPEYLSJMIUV

not attested not anchored not stored refs pending

Approximate groups, III: the unitary case

Ben Green, Emmanuel Breuillard

arxiv:1006.5160 v2 · 2010-06-26 · 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{SJ2O4RGFK2MRB2PPPEYLSJMIUV}

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	2026-05-18T04:31:42.181974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9274ee44c5569910e9ef7930b92588a564b896c31e6e0faeae8e97f3c7802889

Aliases

arxiv: 1006.5160 · arxiv_version: 1006.5160v2 · doi: 10.48550/arxiv.1006.5160 · pith_short_12: SJ2O4RGFK2MR · pith_short_16: SJ2O4RGFK2MRB2PP · pith_short_8: SJ2O4RGF

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/SJ2O4RGFK2MRB2PPPEYLSJMIUV \
  | 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: 9274ee44c5569910e9ef7930b92588a564b896c31e6e0faeae8e97f3c7802889

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca9ae8f7f91cddd0fad031b046419e957e7d0d63a4aa017e5c3d7192fb8eddd5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-26T18:53:41Z",
    "title_canon_sha256": "97d62e5a6a248f34298af0528bb97ce34f101cd498944dcd32c65963f072d089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5160",
    "kind": "arxiv",
    "version": 2
  }
}