Pith Number

pith:F7UPNNSA

pith:2008:F7UPNNSAXXFFIKW3OIFLYF3MQZ

not attested not anchored not stored refs pending

Proof of Ira Gessel's Lattice Path Conjecture

Christoph Koutschan, Doron Zeilberger, Manuel Kauers

arxiv:0806.4300 v1 · 2008-06-26 · 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{F7UPNNSAXXFFIKW3OIFLYF3MQZ}

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	2026-05-18T02:15:46.020770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fe8f6b640bdca542adb720abc176c867b684384471a54a5bfcfe6f951801260

Aliases

arxiv: 0806.4300 · arxiv_version: 0806.4300v1 · doi: 10.48550/arxiv.0806.4300 · pith_short_12: F7UPNNSAXXFF · pith_short_16: F7UPNNSAXXFFIKW3 · pith_short_8: F7UPNNSA

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/F7UPNNSAXXFFIKW3OIFLYF3MQZ \
  | 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: 2fe8f6b640bdca542adb720abc176c867b684384471a54a5bfcfe6f951801260

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a738a803a9c4ee15493d83556156bc8a25b1d8c8dbd6add0a002ad31c51868b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-06-26T15:42:29Z",
    "title_canon_sha256": "8e85a5215f370e2b376fd053fc79541808e873a7a6f7830f06c831dc1dee17fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.4300",
    "kind": "arxiv",
    "version": 1
  }
}