Pith Number

pith:3VHEGEZ6

pith:2009:3VHEGEZ6FU3J2VZYGVPXFNU5GR

not attested not anchored not stored refs pending

Explicit expression for the generating function counting Gessel's walks

Irina Kurkova, Kilian Raschel

arxiv:0912.0457 v3 · 2009-12-02 · math.CO · math.CV · 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{3VHEGEZ6FU3J2VZYGVPXFNU5GR}

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	2026-05-18T04:11:51.972818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd4e43133e2d369d5738355f72b69d3453c7727683e8d08f3316a91f693184af

Aliases

arxiv: 0912.0457 · arxiv_version: 0912.0457v3 · doi: 10.48550/arxiv.0912.0457 · pith_short_12: 3VHEGEZ6FU3J · pith_short_16: 3VHEGEZ6FU3J2VZY · pith_short_8: 3VHEGEZ6

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/3VHEGEZ6FU3J2VZYGVPXFNU5GR \
  | 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: dd4e43133e2d369d5738355f72b69d3453c7727683e8d08f3316a91f693184af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4396db82bca361a39353bb2b9908f2af2cabecdedf046b4fbfe2a51aeb87c211",
    "cross_cats_sorted": [
      "math.CV",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-02T16:33:01Z",
    "title_canon_sha256": "d081df213318910bb3c4ab278416b1e65b73d50fb47368c9df24a29f578695a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0457",
    "kind": "arxiv",
    "version": 3
  }
}