Pith Number

pith:A274G46S

pith:2010:A274G46SYHGIYXFBHOBTEVPQ7L

not attested not anchored not stored refs pending

The probability that $x$ and $y$ commute in a compact group

Darmstadt, Francesco G. Russo (Universita' degli Studi di Palermo, Germany), Italy), Karl H. Hofmann (Technische Universitaet Darmstadt, Palermo

arxiv:1001.4856 v6 · 2010-01-27 · math.GR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A274G46SYHGIYXFBHOBTEVPQ7L}

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	2026-05-18T03:53:17.836937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06bfc373d2c1cc8c5ca13b833255f0fad80a706b214524e69010091cf5352244

Aliases

arxiv: 1001.4856 · arxiv_version: 1001.4856v6 · doi: 10.48550/arxiv.1001.4856 · pith_short_12: A274G46SYHGI · pith_short_16: A274G46SYHGIYXFB · pith_short_8: A274G46S

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/A274G46SYHGIYXFBHOBTEVPQ7L \
  | 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: 06bfc373d2c1cc8c5ca13b833255f0fad80a706b214524e69010091cf5352244

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdd946a7ebaec6b873c36cb6a65daf4d46f87b002902ceccdb39f5d445870d7d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-01-27T05:41:04Z",
    "title_canon_sha256": "b4329096298cc136f871cd193116de73d80851f8efb7eaf4c87827df5ca73ddb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.4856",
    "kind": "arxiv",
    "version": 6
  }
}