Pith Number

pith:XZDF33KU

pith:2009:XZDF33KUJQYV3RQVD2J27XUDCA

not attested not anchored not stored refs pending

Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length

Alexey Muranov

arxiv:0909.2294 v4 · 2009-09-14 · 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{XZDF33KUJQYV3RQVD2J27XUDCA}

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	2026-05-18T04:41:16.391335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be465ded544c315dc6151e93afde83100ef9e44b001617a18656cf7240f03d6c

Aliases

arxiv: 0909.2294 · arxiv_version: 0909.2294v4 · doi: 10.48550/arxiv.0909.2294 · pith_short_12: XZDF33KUJQYV · pith_short_16: XZDF33KUJQYV3RQV · pith_short_8: XZDF33KU

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/XZDF33KUJQYV3RQVD2J27XUDCA \
  | 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: be465ded544c315dc6151e93afde83100ef9e44b001617a18656cf7240f03d6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94c8ba4e1d344d769822ea2f53b6365f0f5b00e13643f6e0ab1362cd328fc429",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-14T10:19:58Z",
    "title_canon_sha256": "877fca05c70bcf5cf1737be979b806f4bdc4dc8597cf3dc8eee0b7c5f52cedbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.2294",
    "kind": "arxiv",
    "version": 4
  }
}