Pith Number

pith:VYTLBDKY

pith:2015:VYTLBDKYCCYBHPDVTXTZGLJZN7

not attested not anchored not stored refs pending

On cyclic associative Abel-Grassman groupoids

Imtiaz Ahmad, Muhammad Iqbal, Muhammad Irfan Ali, Muhammad Shah

arxiv:1510.01316 v1 · 2015-10-05 · 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{VYTLBDKYCCYBHPDVTXTZGLJZN7}

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	2026-05-18T01:30:57.205629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae26b08d5810b013bc759de7932d396fca80e70908b04af7c44c6896b166c53b

Aliases

arxiv: 1510.01316 · arxiv_version: 1510.01316v1 · doi: 10.48550/arxiv.1510.01316 · pith_short_12: VYTLBDKYCCYB · pith_short_16: VYTLBDKYCCYBHPDV · pith_short_8: VYTLBDKY

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/VYTLBDKYCCYBHPDVTXTZGLJZN7 \
  | 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: ae26b08d5810b013bc759de7932d396fca80e70908b04af7c44c6896b166c53b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a95e57e4e4ec7d0da172920eb19cb109b5ad7d21e333fd5b4187770bfb40c599",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-05T10:29:30Z",
    "title_canon_sha256": "3fe03a6c7558fc5513a2df1459eb6718af426b4c26c4f36a5b7b6f3b562bbb81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01316",
    "kind": "arxiv",
    "version": 1
  }
}