Pith Number

pith:43OAHWGQ

pith:2009:43OAHWGQMK4DS2DHXWI7DZETEF

not attested not anchored not stored refs pending

Random permutations with cycle weights

Daniel Ueltschi, Volker Betz, Yvan Velenik

arxiv:0908.2217 v3 · 2009-08-17 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{43OAHWGQMK4DS2DHXWI7DZETEF}

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	2026-05-18T04:32:01.846174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6dc03d8d062b8396867bd91f1e493217e6ec2ecd38bf4d00df5981f2c376d63

Aliases

arxiv: 0908.2217 · arxiv_version: 0908.2217v3 · doi: 10.48550/arxiv.0908.2217 · pith_short_12: 43OAHWGQMK4D · pith_short_16: 43OAHWGQMK4DS2DH · pith_short_8: 43OAHWGQ

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/43OAHWGQMK4DS2DHXWI7DZETEF \
  | 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: e6dc03d8d062b8396867bd91f1e493217e6ec2ecd38bf4d00df5981f2c376d63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad90405fc18e76c31c5d5c7bdde0acbf7543d99ef8e59a7305f1d2242f987158",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-08-17T13:46:55Z",
    "title_canon_sha256": "71c8d77e5e4a63ddbc8bbc390bd167507de09a37f1a1d6b281ca3ad98485028b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.2217",
    "kind": "arxiv",
    "version": 3
  }
}