Pith Number

pith:JZENRFHF

pith:2012:JZENRFHFSBGTEN6C5MGZ6P3POF

not attested not anchored not stored refs pending

Umbral calculus associated with Bernoulli polynomials

Dae San Kim, Taekyun Kim

arxiv:1212.2589 v1 · 2012-12-03 · 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{JZENRFHFSBGTEN6C5MGZ6P3POF}

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	2026-05-18T03:38:44.177658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e48d894e5904d3237c2eb0d9f3f6f71653b026d2c634dfd23ba6207db051aea

Aliases

arxiv: 1212.2589 · arxiv_version: 1212.2589v1 · doi: 10.48550/arxiv.1212.2589 · pith_short_12: JZENRFHFSBGT · pith_short_16: JZENRFHFSBGTEN6C · pith_short_8: JZENRFHF

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/JZENRFHFSBGTEN6C5MGZ6P3POF \
  | 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: 4e48d894e5904d3237c2eb0d9f3f6f71653b026d2c634dfd23ba6207db051aea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8400e64867c374bee6c8d74c88bda9ecdc3a2f1ab93bbff80f879675e9914681",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-03T13:30:56Z",
    "title_canon_sha256": "e934b3f9d468c9f294153465a51fddb8e58ea8ff200b7c6647fdedc6834b729e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2589",
    "kind": "arxiv",
    "version": 1
  }
}