Pith Number

pith:FFCC3MJE

pith:2014:FFCC3MJE4NWB5YBMY6R4A4PB4O

not attested not anchored not stored refs pending

Counting permutations by alternating descents

Ira M. Gessel, Yan Zhuang

arxiv:1408.1886 v1 · 2014-08-08 · 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{FFCC3MJE4NWB5YBMY6R4A4PB4O}

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	2026-05-18T02:45:38.909774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29442db124e36c1ee02cc7a3c071e1e3a9a7e82a732ddef0272b05d34602e04b

Aliases

arxiv: 1408.1886 · arxiv_version: 1408.1886v1 · doi: 10.48550/arxiv.1408.1886 · pith_short_12: FFCC3MJE4NWB · pith_short_16: FFCC3MJE4NWB5YBM · pith_short_8: FFCC3MJE

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/FFCC3MJE4NWB5YBMY6R4A4PB4O \
  | 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: 29442db124e36c1ee02cc7a3c071e1e3a9a7e82a732ddef0272b05d34602e04b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2f081c9f961fa182cc2e0cdd31c90277c250a664ad1b208fe5e5f362f8fbaba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-08-08T15:25:40Z",
    "title_canon_sha256": "3bb9761347c7a39c87ee7c86f58be7fc9df922b179f413e50c16a32ad669d3d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1886",
    "kind": "arxiv",
    "version": 1
  }
}