Pith Number

pith:VEQ5O23E

pith:2012:VEQ5O23ECB2CR6FBLXEXKJ67WV

not attested not anchored not stored refs pending

On the number of cycles in a random permutation

Ashkan Nikeghbali, Dirk Zeindler, Kenneth Maples

arxiv:1203.4132 v1 · 2012-03-19 · 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{VEQ5O23ECB2CR6FBLXEXKJ67WV}

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	2026-05-18T03:15:56.060354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a921d76b64107428f8a15dc97527dfb57ec1ff78f34783710384c22717a5fa81

Aliases

arxiv: 1203.4132 · arxiv_version: 1203.4132v1 · doi: 10.48550/arxiv.1203.4132 · pith_short_12: VEQ5O23ECB2C · pith_short_16: VEQ5O23ECB2CR6FB · pith_short_8: VEQ5O23E

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/VEQ5O23ECB2CR6FBLXEXKJ67WV \
  | 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: a921d76b64107428f8a15dc97527dfb57ec1ff78f34783710384c22717a5fa81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7226ad0e77c7b93872c1e2b3798b4815017eb6f908262747d0361a28c155d3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-19T15:32:12Z",
    "title_canon_sha256": "0c13158dc7d34a7a5979836c4a6c781fc44045a846f64a99d440082d2934b591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4132",
    "kind": "arxiv",
    "version": 1
  }
}