Pith Number

pith:KUPPKQJE

pith:1994:KUPPKQJELLYJ56YCTNTWYTKT4V

not attested not anchored not stored refs pending

Counting pairs of lattice paths by intersections

Herbert S. Wilf, Ira Gessel, Lily Yen, Walter Shur, Wayne Goddard

arxiv:math/9409212 v1 · 1994-09-16 · 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{KUPPKQJELLYJ56YCTNTWYTKT4V}

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	2026-05-18T01:05:51.118991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

551ef541245af09efb029b676c4d53e55792bd6b62618fb90dda6142ab8feeb9

Aliases

arxiv: math/9409212 · arxiv_version: math/9409212v1 · doi: 10.48550/arxiv.math/9409212 · pith_short_12: KUPPKQJELLYJ · pith_short_16: KUPPKQJELLYJ56YC · pith_short_8: KUPPKQJE

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/KUPPKQJELLYJ56YCTNTWYTKT4V \
  | 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: 551ef541245af09efb029b676c4d53e55792bd6b62618fb90dda6142ab8feeb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83f9f54e4113b01fa107543b698cfafd92be4a325ba1da6ddb71e7caf8e6d458",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1994-09-16T00:00:00Z",
    "title_canon_sha256": "39e279346730fd66aa8d22b4f78faeab15805badb3ea36165c21a9c6514dcbba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9409212",
    "kind": "arxiv",
    "version": 1
  }
}