Pith Number

pith:MS2WKOAL

pith:2010:MS2WKOALJDJSQSAAUIBQMIB6BC

not attested not anchored not stored refs pending

Commutativity degree, its generalizations, and classification of finite groups

Ashish Kumar Das, Rajat Kanti Nath

arxiv:1009.5526 v1 · 2010-09-28 · 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{MS2WKOALJDJSQSAAUIBQMIB6BC}

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	2026-05-18T04:40:09.925436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64b565380b48d3284800a20306203e0895e665a1a3326c79ab9d47372ace4695

Aliases

arxiv: 1009.5526 · arxiv_version: 1009.5526v1 · doi: 10.48550/arxiv.1009.5526 · pith_short_12: MS2WKOALJDJS · pith_short_16: MS2WKOALJDJSQSAA · pith_short_8: MS2WKOAL

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/MS2WKOALJDJSQSAAUIBQMIB6BC \
  | 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: 64b565380b48d3284800a20306203e0895e665a1a3326c79ab9d47372ace4695

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7fa3923aca7e3d0237851c7bcaaa5c8101eb6ce5b70218d5c26dde6cd7320d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-28T10:40:32Z",
    "title_canon_sha256": "9b2402476399fc2cf636a46f9d362bda945d07cab9066a83b0aa68324a1e3084"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5526",
    "kind": "arxiv",
    "version": 1
  }
}