Pith Number

pith:F5EBKKOJ

pith:2013:F5EBKKOJ3RHLUHPB7EFOIYV4YJ

not attested not anchored not stored refs pending

Higher-order Bernoulli, Frobenius-Euler and Euler polynomials

Dae San Kim, Taekyun Kim

arxiv:1302.6485 v1 · 2013-02-26 · 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{F5EBKKOJ3RHLUHPB7EFOIYV4YJ}

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	2026-05-18T03:32:29.093406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f481529c9dc4eba1de1f90ae462bcc266ec233c004cff58b8c485ce5361bfb2

Aliases

arxiv: 1302.6485 · arxiv_version: 1302.6485v1 · doi: 10.48550/arxiv.1302.6485 · pith_short_12: F5EBKKOJ3RHL · pith_short_16: F5EBKKOJ3RHLUHPB · pith_short_8: F5EBKKOJ

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/F5EBKKOJ3RHLUHPB7EFOIYV4YJ \
  | 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: 2f481529c9dc4eba1de1f90ae462bcc266ec233c004cff58b8c485ce5361bfb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42acee5bacb9f28876732e31b671ccb2bff4882906679071cab4e5cc85e2014f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-26T16:33:11Z",
    "title_canon_sha256": "ae9536b56af98972fccad0ab0b59112c92afcd1441e7f7685e0b4439b461fe85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.6485",
    "kind": "arxiv",
    "version": 1
  }
}