Pith Number

pith:A24GFD3J

pith:2014:A24GFD3JTTETEO2PNMWLXB4VMB

not attested not anchored not stored refs pending

What is a horocyclic product, and how is it related to lamplighters?

Wolfgang Woess

arxiv:1401.1976 v1 · 2014-01-09 · math.GR · math.CO · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A24GFD3JTTETEO2PNMWLXB4VMB}

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	2026-05-18T03:02:47.908861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06b8628f699cc9323b4f6b2cbb8795605d1103e557b84199c799fb24c2728e63

Aliases

arxiv: 1401.1976 · arxiv_version: 1401.1976v1 · doi: 10.48550/arxiv.1401.1976 · pith_short_12: A24GFD3JTTET · pith_short_16: A24GFD3JTTETEO2P · pith_short_8: A24GFD3J

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/A24GFD3JTTETEO2PNMWLXB4VMB \
  | 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: 06b8628f699cc9323b4f6b2cbb8795605d1103e557b84199c799fb24c2728e63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97f4a6d19b8d2de28ea750d03061b07743bc5bb47249cd3d081d7ca5dcb1d6b7",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-01-09T12:19:44Z",
    "title_canon_sha256": "90cce2d3ccd2a5d76253b77803b5048df78dc9b9c7e69a7e3d70c836ba7d6942"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.1976",
    "kind": "arxiv",
    "version": 1
  }
}