Pith Number

pith:FAJ2EKPV

pith:2014:FAJ2EKPVIZZ7CBPPGIYY6BZLOU

not attested not anchored not stored refs pending

Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers

Bai-Ni Guo, Feng Qi

arxiv:1401.4257 v2 · 2014-01-17 · math.NT · math.CA · 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{FAJ2EKPVIZZ7CBPPGIYY6BZLOU}

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	2026-05-18T02:43:36.548619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2813a229f54673f105ef32318f072b7506977f61d8b4371fd8c61fad74a9ea3e

Aliases

arxiv: 1401.4257 · arxiv_version: 1401.4257v2 · doi: 10.48550/arxiv.1401.4257 · pith_short_12: FAJ2EKPVIZZ7 · pith_short_16: FAJ2EKPVIZZ7CBPP · pith_short_8: FAJ2EKPV

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/FAJ2EKPVIZZ7CBPPGIYY6BZLOU \
  | 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: 2813a229f54673f105ef32318f072b7506977f61d8b4371fd8c61fad74a9ea3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e3273635800d2d6bb76ccaffa05cf76a5845ad15f31b09c64082bca4cfe5190",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-01-17T07:15:16Z",
    "title_canon_sha256": "fe1985c058c62bcff4beb3cb27e88d470259314fd3e3c9e56f7b8fae497ab1ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.4257",
    "kind": "arxiv",
    "version": 2
  }
}