Pith Number

pith:UMJCXNPA

pith:2012:UMJCXNPAOI7U3QCDOXVLDY6QRO

not attested not anchored not stored refs pending

Enumeration of nilpotent loops up to isotopy

Lucien Clavier

arxiv:1201.5659 v2 · 2012-01-26 · 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{UMJCXNPAOI7U3QCDOXVLDY6QRO}

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	2026-05-18T03:46:59.015062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3122bb5e0723f4dc04375eab1e3d08b8ae0dfa218a0df1d1cc96cbd682fee3a

Aliases

arxiv: 1201.5659 · arxiv_version: 1201.5659v2 · doi: 10.48550/arxiv.1201.5659 · pith_short_12: UMJCXNPAOI7U · pith_short_16: UMJCXNPAOI7U3QCD · pith_short_8: UMJCXNPA

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/UMJCXNPAOI7U3QCDOXVLDY6QRO \
  | 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: a3122bb5e0723f4dc04375eab1e3d08b8ae0dfa218a0df1d1cc96cbd682fee3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d457121e9c0cd847b3b4c3d3f501a678366263cc05b927ed681f40872d35a7bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-01-26T21:48:59Z",
    "title_canon_sha256": "38571e34087eb9d5a65a238f485d599b42b97433388d4376ccbf340222dffa54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.5659",
    "kind": "arxiv",
    "version": 2
  }
}