Pith Number

pith:ASH45XCU

pith:2013:ASH45XCUCUSOMWWDKVXAGKU4ZQ

not attested not anchored not stored refs pending

Some identities of higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus

Dae San Kim, Dmitry V. Dolgy, Seog-Hoon Rim, Taekyun Kim

arxiv:1302.5345 v1 · 2013-02-21 · 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{ASH45XCUCUSOMWWDKVXAGKU4ZQ}

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	2026-05-18T03:32:57.922800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

048fcedc541524e65ac3556e032a9ccc232c4f33d5afe6351e68d51fbfdb18a2

Aliases

arxiv: 1302.5345 · arxiv_version: 1302.5345v1 · doi: 10.48550/arxiv.1302.5345 · pith_short_12: ASH45XCUCUSO · pith_short_16: ASH45XCUCUSOMWWD · pith_short_8: ASH45XCU

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/ASH45XCUCUSOMWWDKVXAGKU4ZQ \
  | 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: 048fcedc541524e65ac3556e032a9ccc232c4f33d5afe6351e68d51fbfdb18a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10c25fd548d651d8a782c4a7ef9f322a2085a10c5f1d9b84223fc142dacadd81",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-21T17:15:00Z",
    "title_canon_sha256": "bd6b0a6f65aab8bd29659700b175aea4571d609e53a58500beab5d595de8e768"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5345",
    "kind": "arxiv",
    "version": 1
  }
}