Pith Number

pith:KSGF4G6E

pith:2010:KSGF4G6EA3QE46XQVFVUAMIUZJ

not attested not anchored not stored refs pending

A generalization of the probability that the commutator of two group elements is equal to a given element

Ahmad M. A. Alghamdi (Umm Alqura University, Francesco G. Russo (Universita' degli Studi di Palermo, Italy), Makkah, Palermo, Saudi Arabia)

arxiv:1004.0934 v5 · 2010-04-06 · math.GR · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KSGF4G6EA3QE46XQVFVUAMIUZJ}

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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	2026-05-18T03:33:26.907864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

548c5e1bc406e04e7af0a96b403114ca5f399974eea333c77815b14a74b0482c

Aliases

arxiv: 1004.0934 · arxiv_version: 1004.0934v5 · doi: 10.48550/arxiv.1004.0934 · pith_short_12: KSGF4G6EA3QE · pith_short_16: KSGF4G6EA3QE46XQ · pith_short_8: KSGF4G6E

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/KSGF4G6EA3QE46XQVFVUAMIUZJ \
  | 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: 548c5e1bc406e04e7af0a96b403114ca5f399974eea333c77815b14a74b0482c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10076dc8b32754d9793563007dd2f2e577a9c82e786bf1b33eb0898586bd1e6e",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-04-06T19:20:53Z",
    "title_canon_sha256": "39c886ad15aee999f2311ab30243f2873cefea5e52303ae405128eca30a6581d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0934",
    "kind": "arxiv",
    "version": 5
  }
}