Pith Number

pith:NTMFB4M4

pith:2011:NTMFB4M4CTXK2QCSALXD7FI6QO

not attested not anchored not stored refs pending

Examples of Abel Grassmann's groupoids

Madad Khan, Qaiser Mushtaq, Sameera Bano

arxiv:1101.0949 v1 · 2011-01-05 · 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{NTMFB4M4CTXK2QCSALXD7FI6QO}

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	2026-05-18T04:32:01.112942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cd850f19c14eead405202ee3f951e838af21351bc4a2010805e2a5f1fb93c39

Aliases

arxiv: 1101.0949 · arxiv_version: 1101.0949v1 · doi: 10.48550/arxiv.1101.0949 · pith_short_12: NTMFB4M4CTXK · pith_short_16: NTMFB4M4CTXK2QCS · pith_short_8: NTMFB4M4

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/NTMFB4M4CTXK2QCSALXD7FI6QO \
  | 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: 6cd850f19c14eead405202ee3f951e838af21351bc4a2010805e2a5f1fb93c39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a65f44ae47257f8fc15f2ec0d724d90c8e0f50688c92c3a33c0ec6573a0e21d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-01-05T12:38:43Z",
    "title_canon_sha256": "84396ed11c3cbb44da091cdea3835f3649290363083303815a982a4f688d4774"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0949",
    "kind": "arxiv",
    "version": 1
  }
}