Pith Number

pith:ZHFEJJC2

pith:2018:ZHFEJJC2WHYY7I2SRZFK4NQS3N

not attested not anchored not stored refs pending

Reciprocals of exponential polynomials and permutation enumeration

Ira M. Gessel

arxiv:1807.09290 v3 · 2018-07-24 · 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{ZHFEJJC2WHYY7I2SRZFK4NQS3N}

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	2026-05-17T23:45:52.971863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9ca44a45ab1f18fa3528e4aae3612db7c29feaf1655aee3f7b46cc1de117d6f

Aliases

arxiv: 1807.09290 · arxiv_version: 1807.09290v3 · doi: 10.48550/arxiv.1807.09290 · pith_short_12: ZHFEJJC2WHYY · pith_short_16: ZHFEJJC2WHYY7I2S · pith_short_8: ZHFEJJC2

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/ZHFEJJC2WHYY7I2SRZFK4NQS3N \
  | 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: c9ca44a45ab1f18fa3528e4aae3612db7c29feaf1655aee3f7b46cc1de117d6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acee80c1d810621c76f5ee71646b920f828e3136cc36a1ba89c804bee19fa544",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-24T18:09:17Z",
    "title_canon_sha256": "f4fc623f14b6e2a5d4c09f7e16206098299bd96af9611e9e3964353ad473f1d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.09290",
    "kind": "arxiv",
    "version": 3
  }
}