Pith Number

pith:LAUAGM7A

pith:2015:LAUAGM7AHPEMGM5X2AOKR35HLE

not attested not anchored not stored refs pending

Two closed forms for the Apostol-Bernoulli polynomials

Min-Soo Kim, Su Hu

arxiv:1509.04190 v6 · 2015-09-14 · math.CO · math.CA · 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{LAUAGM7AHPEMGM5X2AOKR35HLE}

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	2026-05-18T00:07:51.273034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58280333e03bc8c333b7d01ca8efa75904a68d2b826e978fea18e0b53cbb2c60

Aliases

arxiv: 1509.04190 · arxiv_version: 1509.04190v6 · doi: 10.48550/arxiv.1509.04190 · pith_short_12: LAUAGM7AHPEM · pith_short_16: LAUAGM7AHPEMGM5X · pith_short_8: LAUAGM7A

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/LAUAGM7AHPEMGM5X2AOKR35HLE \
  | 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: 58280333e03bc8c333b7d01ca8efa75904a68d2b826e978fea18e0b53cbb2c60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9364619cf297fcd327787281d29519ec2e7203c710204be820cb0adcee5e1b22",
    "cross_cats_sorted": [
      "math.CA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-14T16:39:54Z",
    "title_canon_sha256": "178ac1fc03834e933d40413eef0e3661f962b1ca0fb3407f6768ee54e03a88e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04190",
    "kind": "arxiv",
    "version": 6
  }
}