Pith Number

pith:4LNC3L5B

pith:2014:4LNC3L5BM6QLGP2R7CFVOCKOGV

not attested not anchored not stored refs pending

On the condensation property of the Lamplighter groups and groups of Intermediate growth

Mustafa Gokhan Benli, Rostislav Grigorchuk

arxiv:1405.1680 v1 · 2014-05-07 · 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{4LNC3L5BM6QLGP2R7CFVOCKOGV}

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	2026-05-18T02:52:24.146584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2da2dafa167a0b33f51f88b57094e35461a8178be2397ade7cfee7dd308817a

Aliases

arxiv: 1405.1680 · arxiv_version: 1405.1680v1 · doi: 10.48550/arxiv.1405.1680 · pith_short_12: 4LNC3L5BM6QL · pith_short_16: 4LNC3L5BM6QLGP2R · pith_short_8: 4LNC3L5B

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/4LNC3L5BM6QLGP2R7CFVOCKOGV \
  | 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: e2da2dafa167a0b33f51f88b57094e35461a8178be2397ade7cfee7dd308817a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69f2f2e56285d90764efe99ed204a5ec39c170c7f120f28f7da0a36c1fab658a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-05-07T17:53:30Z",
    "title_canon_sha256": "0c22a006bf34b6cbc3e922e5c41568f5ef161c4f51de639628f6a8ebab8c45f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.1680",
    "kind": "arxiv",
    "version": 1
  }
}