Pith Number

pith:HWNMJMJS

pith:2009:HWNMJMJSDTCDXDWIUAMWCFTX3P

not attested not anchored not stored refs pending

Uniquely 2-divisible Bol loops

Michael Kinyon, Tuval Foguel

arxiv:0910.2429 v4 · 2009-10-13 · 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{HWNMJMJSDTCDXDWIUAMWCFTX3P}

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	2026-05-18T04:15:17.107660Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d9ac4b1321cc43b8ec8a019611677dbdb27f247215ec176a04870ae3eaa1cc9

Aliases

arxiv: 0910.2429 · arxiv_version: 0910.2429v4 · doi: 10.48550/arxiv.0910.2429 · pith_short_12: HWNMJMJSDTCD · pith_short_16: HWNMJMJSDTCDXDWI · pith_short_8: HWNMJMJS

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/HWNMJMJSDTCDXDWIUAMWCFTX3P \
  | 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: 3d9ac4b1321cc43b8ec8a019611677dbdb27f247215ec176a04870ae3eaa1cc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1924ed56462f4c3327031068e973fd018084540754309f2d2d72c7e88bd1e56",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-10-13T19:36:07Z",
    "title_canon_sha256": "c854bd440ad886bba7b527d7a8ec01765a60d007a8f3684c1fd17850c156b6e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.2429",
    "kind": "arxiv",
    "version": 4
  }
}