Pith Number

pith:DRJ7XAJ7

pith:2010:DRJ7XAJ7EEP7AZSTQFQ4TFQ3GK

not attested not anchored not stored refs pending

Strongly dense free subgroups of semisimple algebraic groups

Ben Green, Emmanuel Breuillard, Robert Guralnick, Terence Tao

arxiv:1010.4259 v3 · 2010-10-20 · math.GR · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DRJ7XAJ7EEP7AZSTQFQ4TFQ3GK}

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	2026-05-18T04:25:49.164249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c53fb813f211ff066538161c9961b32a090950e1eee50f6b81d39c100fbdb46

Aliases

arxiv: 1010.4259 · arxiv_version: 1010.4259v3 · doi: 10.48550/arxiv.1010.4259 · pith_short_12: DRJ7XAJ7EEP7 · pith_short_16: DRJ7XAJ7EEP7AZST · pith_short_8: DRJ7XAJ7

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/DRJ7XAJ7EEP7AZSTQFQ4TFQ3GK \
  | 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: 1c53fb813f211ff066538161c9961b32a090950e1eee50f6b81d39c100fbdb46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "508f654c64c1c0cd9b5980eec1d121a41721976ff797d18852a4806bd18468a6",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-10-20T17:39:42Z",
    "title_canon_sha256": "7ceee806300ef56e0bb6d25a9ea959261844350d98e7a0e66809d1cad6cf4c14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4259",
    "kind": "arxiv",
    "version": 3
  }
}