Pith Number

pith:7DWPM7BM

pith:2011:7DWPM7BMVW244EZ3BIO4WZ27WE

not attested not anchored not stored refs pending

Cycle structure of random permutations with cycle weights

Daniel Ueltschi, Nicholas M. Ercolani

arxiv:1102.4796 v2 · 2011-02-23 · 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{7DWPM7BMVW244EZ3BIO4WZ27WE}

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	2026-05-18T03:06:05.150305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8ecf67c2cadb5ce133b0a1dcb675fb13906a857be5180cc2954a4c86b819018

Aliases

arxiv: 1102.4796 · arxiv_version: 1102.4796v2 · doi: 10.48550/arxiv.1102.4796 · pith_short_12: 7DWPM7BMVW24 · pith_short_16: 7DWPM7BMVW244EZ3 · pith_short_8: 7DWPM7BM

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/7DWPM7BMVW244EZ3BIO4WZ27WE \
  | 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: f8ecf67c2cadb5ce133b0a1dcb675fb13906a857be5180cc2954a4c86b819018

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4ace0e58892dddd9d787f869d699dd341e02efed09c3de0e83096862dd569c7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-23T16:56:45Z",
    "title_canon_sha256": "15fcdcb6f72025bb6e693d07dc6a8dbab181f247866c5ed81457ea03c75ed132"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4796",
    "kind": "arxiv",
    "version": 2
  }
}