Pith Number

pith:Y4A4HFJO

pith:2013:Y4A4HFJOGWZSFWUD2PJNULPIEK

not attested not anchored not stored refs pending

A few remarks on Euler and Bernoulli polynomials and their connections with binomial coefficients and modified Pascal matrices

Pawe{\l} J. Szab{\l}owski

arxiv:1307.0300 v1 · 2013-07-01 · math.RA · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y4A4HFJOGWZSFWUD2PJNULPIEK}

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	2026-05-18T02:57:06.687871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c701c3952e35b322da83d3d2da2de822aaba91849bcb556dbd434cc1a375ae72

Aliases

arxiv: 1307.0300 · arxiv_version: 1307.0300v1 · doi: 10.48550/arxiv.1307.0300 · pith_short_12: Y4A4HFJOGWZS · pith_short_16: Y4A4HFJOGWZSFWUD · pith_short_8: Y4A4HFJO

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/Y4A4HFJOGWZSFWUD2PJNULPIEK \
  | 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: c701c3952e35b322da83d3d2da2de822aaba91849bcb556dbd434cc1a375ae72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9829b016f9a0fe7654757945665da7bf40c1f358774aa1053d3ea06785d9158",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-07-01T08:40:12Z",
    "title_canon_sha256": "2948ae4d5a54656271e114171ff18a7373c20a9544dd15f249bacc26e2646f2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0300",
    "kind": "arxiv",
    "version": 1
  }
}