Pith Number

pith:264VYY6Q

pith:2013:264VYY6QQHUN76KN2PP2FLPAPA

not attested not anchored not stored refs pending

Apostol-Euler polynomials arising from umbral calculus

Seog-Hoon Rim, Taekyun Kim, Toufik Mansour

arxiv:1302.3104 v1 · 2013-02-13 · 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{264VYY6QQHUN76KN2PP2FLPAPA}

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	2026-05-18T03:33:48.741420Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7b95c63d081e8dff94dd3dfa2ade07838c716a87026fa166cf0ce74a902e2c2

Aliases

arxiv: 1302.3104 · arxiv_version: 1302.3104v1 · doi: 10.48550/arxiv.1302.3104 · pith_short_12: 264VYY6QQHUN · pith_short_16: 264VYY6QQHUN76KN · pith_short_8: 264VYY6Q

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/264VYY6QQHUN76KN2PP2FLPAPA \
  | 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: d7b95c63d081e8dff94dd3dfa2ade07838c716a87026fa166cf0ce74a902e2c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b78fe5ec79fcf3ee3eb30c24a2b199739482a5ee16162cb4e492ca3452094e41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-13T14:11:49Z",
    "title_canon_sha256": "5bf6b04bea6324698dc991337e69bbf5258b65d150ef17a296774d097050e1a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.3104",
    "kind": "arxiv",
    "version": 1
  }
}