Pith Number

pith:JV4MQWTN

pith:2018:JV4MQWTNST7RKMK3ZZ443NEOC3

not attested not anchored not stored refs pending

An explicit Formula for Bernoulli Polynomials with a $q$ Parameter in Terms of $r$-Whitney Numbers

F. A. Shiha

arxiv:1804.05437 v1 · 2018-04-15 · 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{JV4MQWTNST7RKMK3ZZ443NEOC3}

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	2026-05-18T00:00:39.635672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d78c85a6d94ff15315bce79cdb48e16e80f6f1fbf077a789914b6bb0ffba436

Aliases

arxiv: 1804.05437 · arxiv_version: 1804.05437v1 · doi: 10.48550/arxiv.1804.05437 · pith_short_12: JV4MQWTNST7R · pith_short_16: JV4MQWTNST7RKMK3 · pith_short_8: JV4MQWTN

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/JV4MQWTNST7RKMK3ZZ443NEOC3 \
  | 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: 4d78c85a6d94ff15315bce79cdb48e16e80f6f1fbf077a789914b6bb0ffba436

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dd2fc370be8b688482b2a8ac7f13bea8c781c90f24054da8f481b38a0c36cc3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-15T22:00:47Z",
    "title_canon_sha256": "f327986137425996e83bd289ce9fc6d586c770773971342944a4f0089233fcd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.05437",
    "kind": "arxiv",
    "version": 1
  }
}