Pith Number

pith:5V7CPZN3

pith:2012:5V7CPZN3YM4BJXXORG2XYKQSF5

not attested not anchored not stored refs pending

Invariant random subgroups of the lamplighter group

Lewis Bowen, Rostislav Grigorchuk, Rostyslav Kravchenko

arxiv:1206.6780 v3 · 2012-06-28 · 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{5V7CPZN3YM4BJXXORG2XYKQSF5}

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	2026-05-18T03:14:28.142679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed7e27e5bbc33814deee89b57c2a122f482cc18e6784ce82ac6a9b4418d6bca1

Aliases

arxiv: 1206.6780 · arxiv_version: 1206.6780v3 · doi: 10.48550/arxiv.1206.6780 · pith_short_12: 5V7CPZN3YM4B · pith_short_16: 5V7CPZN3YM4BJXXO · pith_short_8: 5V7CPZN3

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/5V7CPZN3YM4BJXXORG2XYKQSF5 \
  | 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: ed7e27e5bbc33814deee89b57c2a122f482cc18e6784ce82ac6a9b4418d6bca1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba85791bde4ede9c2715c7828b817eb689d6c7d446fc4a09079edd3db6e82213",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-06-28T18:00:29Z",
    "title_canon_sha256": "796d466b4d15792224abf7b3c05231c080ee83fe769a8d466a514330188f38ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.6780",
    "kind": "arxiv",
    "version": 3
  }
}