Pith Number

pith:TQAKGLXB

pith:2011:TQAKGLXBKJWDBKE3FYTBGRDOBD

not attested not anchored not stored refs pending

Ideal mixture approximation of cluster size distributions at low density

S. Jansen, W. K\"onig

arxiv:1112.4725 v1 · 2011-12-20 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQAKGLXBKJWDBKE3FYTBGRDOBD}

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	2026-05-18T03:52:53.163167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c00a32ee1526c30a89b2e2613446e08f3bdb4e92cedf2d9c29582e823150c29

Aliases

arxiv: 1112.4725 · arxiv_version: 1112.4725v1 · doi: 10.48550/arxiv.1112.4725 · pith_short_12: TQAKGLXBKJWD · pith_short_16: TQAKGLXBKJWDBKE3 · pith_short_8: TQAKGLXB

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/TQAKGLXBKJWDBKE3FYTBGRDOBD \
  | 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: 9c00a32ee1526c30a89b2e2613446e08f3bdb4e92cedf2d9c29582e823150c29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08a56ef45bd57095c2d3d7199859b0affb306b0415bb3a0a5fea24bd6ed462ce",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-12-20T15:26:49Z",
    "title_canon_sha256": "8724de145738be0d8fc05f784c07b140c8059ba4ca18ded733b0064054679bde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4725",
    "kind": "arxiv",
    "version": 1
  }
}