Pith Number

pith:QW2LJGPE

pith:2012:QW2LJGPE3RJLDEMIST4FEW5YZ2

not attested not anchored not stored refs pending

Commutators cannot be proper powers in metric small-cancellation torsion-free groups

Anton A. Klyachko, Elizaveta Frenkel

arxiv:1210.7908 v3 · 2012-10-30 · 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{QW2LJGPE3RJLDEMIST4FEW5YZ2}

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	2026-05-18T03:13:23.639160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85b4b499e4dc52b1918894f8525bb8cea3d861431eb3b5af0ee288883c83ab17

Aliases

arxiv: 1210.7908 · arxiv_version: 1210.7908v3 · doi: 10.48550/arxiv.1210.7908 · pith_short_12: QW2LJGPE3RJL · pith_short_16: QW2LJGPE3RJLDEMI · pith_short_8: QW2LJGPE

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/QW2LJGPE3RJLDEMIST4FEW5YZ2 \
  | 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: 85b4b499e4dc52b1918894f8525bb8cea3d861431eb3b5af0ee288883c83ab17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec86bb9895f5054289e58620660d6eda5dc8a718c531a387048acef1ee7ec711",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-30T05:53:48Z",
    "title_canon_sha256": "07d44e32d09a4e0993db7f523729c100b328a7c922b2fa7bf4b9909552718c7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7908",
    "kind": "arxiv",
    "version": 3
  }
}