Pith Number

pith:QP3ZLQKO

pith:2018:QP3ZLQKOINN65HPIEPASAG6P2C

not attested not anchored not stored refs pending

Some Double Sums Involving Ratios of Binomial Coefficients Arising From Urn Models

David Stenlund, James G. Wan

arxiv:1809.09634 v1 · 2018-09-25 · 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{QP3ZLQKOINN65HPIEPASAG6P2C}

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	2026-05-18T00:04:44.180467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83f795c14e435bee9de823c1201bcfd08d20130aed4a1ef2f48b069291e03a2c

Aliases

arxiv: 1809.09634 · arxiv_version: 1809.09634v1 · doi: 10.48550/arxiv.1809.09634 · pith_short_12: QP3ZLQKOINN6 · pith_short_16: QP3ZLQKOINN65HPI · pith_short_8: QP3ZLQKO

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/QP3ZLQKOINN65HPIEPASAG6P2C \
  | 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: 83f795c14e435bee9de823c1201bcfd08d20130aed4a1ef2f48b069291e03a2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f022566ee9db3c36be48a598de8cc964bbc06d37ff8522ebe687ac7135c2e24c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-09-25T18:00:20Z",
    "title_canon_sha256": "58d7b704d3e44313facfd3b172ac7fd01e93fea1f2ae0d16fb7b1f41f8ce5ec0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.09634",
    "kind": "arxiv",
    "version": 1
  }
}