Pith Number

pith:UDGOT33U

pith:2012:UDGOT33UDZ4Z2BVW32JH75E36K

not attested not anchored not stored refs pending

Some identities for Bernoulli polynomials involving Chebyshev polynomials

Dae San Kim, Sang-Hun Lee, Taekyun Kim

arxiv:1211.1582 v1 · 2012-11-06 · 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{UDGOT33UDZ4Z2BVW32JH75E36K}

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	2026-05-18T03:41:20.683913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0cce9ef741e799d06b6de927ff49bf28e2373bc311e8b9b47731d7280305052

Aliases

arxiv: 1211.1582 · arxiv_version: 1211.1582v1 · doi: 10.48550/arxiv.1211.1582 · pith_short_12: UDGOT33UDZ4Z · pith_short_16: UDGOT33UDZ4Z2BVW · pith_short_8: UDGOT33U

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/UDGOT33UDZ4Z2BVW32JH75E36K \
  | 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: a0cce9ef741e799d06b6de927ff49bf28e2373bc311e8b9b47731d7280305052

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d4af2ac0c409ab696f5378b63bc8e9ad527e1ceb9f9d765134762cdbada44be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-06T16:13:03Z",
    "title_canon_sha256": "5f2d6f9b601da6f2ca9f9b882b0efca70086ce64c6afb4d5a3c839bfd442668c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1582",
    "kind": "arxiv",
    "version": 1
  }
}