Pith Number

pith:4T4UMVJI

pith:2013:4T4UMVJIOZABINMN3Q6BWLO3IC

not attested not anchored not stored refs pending

On growth of random groups of intermediate growth

Mustafa G. Benli, Rostislav Grigorchuk, Yaroslav Vorobets

arxiv:1303.1560 v2 · 2013-03-06 · math.GR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4T4UMVJIOZABINMN3Q6BWLO3IC}

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	2026-05-18T03:26:40.804046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4f9465528764014358ddc3c1b2ddb40a7695954804038e9ddf886219872ca2f

Aliases

arxiv: 1303.1560 · arxiv_version: 1303.1560v2 · doi: 10.48550/arxiv.1303.1560 · pith_short_12: 4T4UMVJIOZAB · pith_short_16: 4T4UMVJIOZABINMN · pith_short_8: 4T4UMVJI

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/4T4UMVJIOZABINMN3Q6BWLO3IC \
  | 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: e4f9465528764014358ddc3c1b2ddb40a7695954804038e9ddf886219872ca2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "670035effc0edd956f5f72acc0b6be240774ea26990c2a8ddf62cd5a5b105576",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-03-06T22:22:42Z",
    "title_canon_sha256": "b8ec9085aa4e41f7d192fed2b0dba2b44805e130211f7fb1bd73ce3709f5212a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1560",
    "kind": "arxiv",
    "version": 2
  }
}