Pith Number

pith:U4VBDX7N

pith:2018:U4VBDX7N44WSVIBSZQYBTDOORL

not attested not anchored not stored refs pending

The 2-variable unified family of generalized Apostol-Euler, Bernoulli and Genocchi polynomials

Alia M. Magar, Beih S. El-Desouky, Rabab S. Gomaa

arxiv:1811.06359 v1 · 2018-11-05 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U4VBDX7N44WSVIBSZQYBTDOORL}

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	2026-05-18T00:00:37.935971Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a72a11dfede72d2aa032cc30198dce8ac4308adfa7fab9cd1b9ca5fe94061b24

Aliases

arxiv: 1811.06359 · arxiv_version: 1811.06359v1 · doi: 10.48550/arxiv.1811.06359 · pith_short_12: U4VBDX7N44WS · pith_short_16: U4VBDX7N44WSVIBS · pith_short_8: U4VBDX7N

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/U4VBDX7N44WSVIBSZQYBTDOORL \
  | 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: a72a11dfede72d2aa032cc30198dce8ac4308adfa7fab9cd1b9ca5fe94061b24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc94b43ef387c808607d3998940ce66157e820fc479e5b63f32bcfb2cabf5156",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-11-05T14:34:29Z",
    "title_canon_sha256": "f05fae3b32dd8b462ecd84ec476c7debaf22a2535bae1e5703d35bf92c315c7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.06359",
    "kind": "arxiv",
    "version": 1
  }
}