Pith Number

pith:5DHPUJGZ

pith:2013:5DHPUJGZFDQ6WVC4RQO2N52US5

not attested not anchored not stored refs pending

On the Asymptotic Statistics of the Number of Occurrences of Multiple Permutation Patterns

Brian Nakamura, Doron Zeilberger, Svante Janson

arxiv:1312.3955 v1 · 2013-12-13 · math.CO · 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{5DHPUJGZFDQ6WVC4RQO2N52US5}

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	2026-05-18T03:04:36.482757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8cefa24d928e1eb545c8c1da6f7549741c8b0a5d4beb1d1c7576c8ab19cd5e7

Aliases

arxiv: 1312.3955 · arxiv_version: 1312.3955v1 · doi: 10.48550/arxiv.1312.3955 · pith_short_12: 5DHPUJGZFDQ6 · pith_short_16: 5DHPUJGZFDQ6WVC4 · pith_short_8: 5DHPUJGZ

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/5DHPUJGZFDQ6WVC4RQO2N52US5 \
  | 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: e8cefa24d928e1eb545c8c1da6f7549741c8b0a5d4beb1d1c7576c8ab19cd5e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "823ccba4fc9dec057004411bc8ff4ec3b6c75b28e28d607605a28439cf8e4008",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-13T21:15:35Z",
    "title_canon_sha256": "f0729c37c0d38a4c5fe8502a328382a4c3ea8e7b38873218b3f1bc3ed07448ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3955",
    "kind": "arxiv",
    "version": 1
  }
}