Pith Number

pith:6RGJHTUP

pith:2012:6RGJHTUPGQHS5G3VUGOUGMDFW5

not attested not anchored not stored refs pending

Umbral calculus and Euler polynomials

Dae San Kim, Seog-Hoon Rim, Taekyun Kim

arxiv:1211.6639 v1 · 2012-11-22 · 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{6RGJHTUPGQHS5G3VUGOUGMDFW5}

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	2026-05-18T03:39:44.140085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f44c93ce8f340f2e9b75a19d433065b74a38fc687da4155eb948f9438ddb370c

Aliases

arxiv: 1211.6639 · arxiv_version: 1211.6639v1 · doi: 10.48550/arxiv.1211.6639 · pith_short_12: 6RGJHTUPGQHS · pith_short_16: 6RGJHTUPGQHS5G3V · pith_short_8: 6RGJHTUP

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/6RGJHTUPGQHS5G3VUGOUGMDFW5 \
  | 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: f44c93ce8f340f2e9b75a19d433065b74a38fc687da4155eb948f9438ddb370c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a458a41fda040575c474e3e71cf172794917be6f23b99bb2431591a3cea19365",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-22T02:37:21Z",
    "title_canon_sha256": "80a92f828b09a7e59b553f14ee121288f04239183e641e21f45d4119738ca5df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6639",
    "kind": "arxiv",
    "version": 1
  }
}