Pith Number

pith:ENGRZVZH

pith:2012:ENGRZVZHRMQGXTXZLP3EP6S6ZE

not attested not anchored not stored refs pending

Amenable groups without finitely presented amenable covers

Mustafa Gokhan Benli, Pierre de la Harpe, Rostislav Grigorchuk

arxiv:1206.2072 v3 · 2012-06-11 · 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{ENGRZVZHRMQGXTXZLP3EP6S6ZE}

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	2026-05-18T03:26:33.812984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

234d1cd7278b206bcef95bf647fa5ec91e259e57e0f0e49da8b7052e7ed6bf08

Aliases

arxiv: 1206.2072 · arxiv_version: 1206.2072v3 · doi: 10.48550/arxiv.1206.2072 · pith_short_12: ENGRZVZHRMQG · pith_short_16: ENGRZVZHRMQGXTXZ · pith_short_8: ENGRZVZH

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/ENGRZVZHRMQGXTXZLP3EP6S6ZE \
  | 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: 234d1cd7278b206bcef95bf647fa5ec91e259e57e0f0e49da8b7052e7ed6bf08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e8c6356130a2f6a5150036e4f964c61becc2185b6a9bcbc112c558e656d7a57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-06-11T00:21:41Z",
    "title_canon_sha256": "36ba86f452958f8859c1d113fce4a5b1533c16e85295cd265b06994014e4a77b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2072",
    "kind": "arxiv",
    "version": 3
  }
}