Pith Number

pith:XOU77752

pith:2013:XOU777524D6JJ4SE2STRZ3UZAL

not attested not anchored not stored refs pending

An integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind

Feng Qi, Xiao-Jing Zhang

arxiv:1301.6425 v2 · 2013-01-28 · math.CA · math.CO · math.CV · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XOU777524D6JJ4SE2STRZ3UZAL}

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	2026-05-18T02:03:48.693245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bba9ffffbae0fc94f244d4a71cee9902c77bc133551a8d06a47c72320130f26a

Aliases

arxiv: 1301.6425 · arxiv_version: 1301.6425v2 · doi: 10.48550/arxiv.1301.6425 · pith_short_12: XOU777524D6J · pith_short_16: XOU777524D6JJ4SE · pith_short_8: XOU77752

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/XOU777524D6JJ4SE2STRZ3UZAL \
  | 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: bba9ffffbae0fc94f244d4a71cee9902c77bc133551a8d06a47c72320130f26a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c86c49ab464353c8abe62ec5712a9dc4fc386ea17b3def69ba2fba1e510db3e",
    "cross_cats_sorted": [
      "math.CO",
      "math.CV",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-01-28T01:44:42Z",
    "title_canon_sha256": "2a09923b237f1b06d1e823ffc4d636e05d211335649b8c56ad743af77d8b3d0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.6425",
    "kind": "arxiv",
    "version": 2
  }
}