Pith Number

pith:FGK4P43H

pith:2013:FGK4P43H57WRUY4G4WK6M4DKIM

not attested not anchored not stored refs pending

Even and Odd Pairs of Lattice Paths with Multiple Intersections

Ira M. Gessel, Walter Shur

arxiv:1301.7714 v1 · 2013-01-31 · 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{FGK4P43H57WRUY4G4WK6M4DKIM}

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	2026-05-18T03:34:48.861976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2995c7f367efed1a6386e595e6706a4312194f846d73d27e017db2ecd6870922

Aliases

arxiv: 1301.7714 · arxiv_version: 1301.7714v1 · doi: 10.48550/arxiv.1301.7714 · pith_short_12: FGK4P43H57WR · pith_short_16: FGK4P43H57WRUY4G · pith_short_8: FGK4P43H

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/FGK4P43H57WRUY4G4WK6M4DKIM \
  | 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: 2995c7f367efed1a6386e595e6706a4312194f846d73d27e017db2ecd6870922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "699b2fed02d01f7b55a7152084dd934825f6a8d27d14c390aecc1bd5867991ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-01-31T18:29:15Z",
    "title_canon_sha256": "3e2d6aa3af4231db5fc72eec5afd556959c457bf0c7c4e6d2359bfdf3c5f0654"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.7714",
    "kind": "arxiv",
    "version": 1
  }
}