Pith Number

pith:3HC3SXRS

pith:2013:3HC3SXRS6JTVDSOQDHOQVKO56L

not attested not anchored not stored refs pending

A human proof of Gessel's lattice path conjecture

Alin Bostan, Irina Kurkova, Kilian Raschel

arxiv:1309.1023 v4 · 2013-09-04 · 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{3HC3SXRS6JTVDSOQDHOQVKO56L}

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	2026-05-18T00:53:51.624185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9c5b95e32f26751c9d019dd0aa9ddf2e0e2d902c93c20da04229316ff97d15a

Aliases

arxiv: 1309.1023 · arxiv_version: 1309.1023v4 · doi: 10.48550/arxiv.1309.1023 · pith_short_12: 3HC3SXRS6JTV · pith_short_16: 3HC3SXRS6JTVDSOQ · pith_short_8: 3HC3SXRS

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/3HC3SXRS6JTVDSOQDHOQVKO56L \
  | 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: d9c5b95e32f26751c9d019dd0aa9ddf2e0e2d902c93c20da04229316ff97d15a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44057096ff0b7d1cd5672d6adfe7219a447dcbf1550ff654bc04626bf663aec3",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-04T13:33:04Z",
    "title_canon_sha256": "3e64bd0f6e9c387b4da42f68acdcfd872a373be68bbbaf2a88cc757675932897"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1023",
    "kind": "arxiv",
    "version": 4
  }
}