Pith Number

pith:NCTV3WHU

pith:2010:NCTV3WHUP6CH6TXSDIWU6YQ3QM

not attested not anchored not stored refs pending

Abel-Grassmann's groupoids characterized by (\in ,\in \vee q_{k}) fuzzy bi-ideals

Kifayat Ullah, Madad Khan

arxiv:1010.3877 v1 · 2010-10-19 · 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{NCTV3WHUP6CH6TXSDIWU6YQ3QM}

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	2026-05-18T04:39:07.365615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68a75dd8f47f847f4ef21a2d4f621b833fc105dee36549e8bb65b7dda2eab7eb

Aliases

arxiv: 1010.3877 · arxiv_version: 1010.3877v1 · doi: 10.48550/arxiv.1010.3877 · pith_short_12: NCTV3WHUP6CH · pith_short_16: NCTV3WHUP6CH6TXS · pith_short_8: NCTV3WHU

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/NCTV3WHUP6CH6TXSDIWU6YQ3QM \
  | 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: 68a75dd8f47f847f4ef21a2d4f621b833fc105dee36549e8bb65b7dda2eab7eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fefce148be27b9d0751de108ca1bb00e2624a681abc11265bad402a0bb05ec1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-10-19T12:33:15Z",
    "title_canon_sha256": "fc106c0a084ddefab82da73cfe12f3041e4cdf2150e1140f1c99305484f8c34d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3877",
    "kind": "arxiv",
    "version": 1
  }
}