Pith Number

pith:WUB4GXO7

pith:2011:WUB4GXO7A2QLYON34MLTR2JUCQ

not attested not anchored not stored refs pending

On the functions counting walks with small steps in the quarter plane

Irina Kurkova, Kilian Raschel

arxiv:1107.2340 v3 · 2011-07-12 · 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{WUB4GXO7A2QLYON34MLTR2JUCQ}

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	2026-05-18T03:41:40.482568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b503c35ddf06a0bc39bbe31738e93414149371d88361c7d4fbeb07133403341f

Aliases

arxiv: 1107.2340 · arxiv_version: 1107.2340v3 · doi: 10.48550/arxiv.1107.2340 · pith_short_12: WUB4GXO7A2QL · pith_short_16: WUB4GXO7A2QLYON3 · pith_short_8: WUB4GXO7

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/WUB4GXO7A2QLYON34MLTR2JUCQ \
  | 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: b503c35ddf06a0bc39bbe31738e93414149371d88361c7d4fbeb07133403341f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f894085a26def45eb918fabd1bfe0eaf799bb02cc9a80eee6d376669a41042f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-12T16:26:44Z",
    "title_canon_sha256": "3f054c058f079114ffa318284bd9fe601d5a8cd4bd72a1173bf56ed3c60f0ea7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2340",
    "kind": "arxiv",
    "version": 3
  }
}