Pith Number

pith:GEJ7E5GU

pith:2011:GEJ7E5GUY4ETR6YXUYHK6TTQYD

not attested not anchored not stored refs pending

Bernoulli type polynomials on Umbral Algebra

Rahime Dere, Yilmaz Simsek

arxiv:1110.1484 v1 · 2011-10-07 · 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{GEJ7E5GUY4ETR6YXUYHK6TTQYD}

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	2026-05-18T00:00:37.450652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3113f274d4c70938fb17a60eaf4e70c0eb335e83ba3c0e4fe92db90dc241ae22

Aliases

arxiv: 1110.1484 · arxiv_version: 1110.1484v1 · doi: 10.48550/arxiv.1110.1484 · pith_short_12: GEJ7E5GUY4ET · pith_short_16: GEJ7E5GUY4ETR6YX · pith_short_8: GEJ7E5GU

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/GEJ7E5GUY4ETR6YXUYHK6TTQYD \
  | 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: 3113f274d4c70938fb17a60eaf4e70c0eb335e83ba3c0e4fe92db90dc241ae22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4625d87a49248289778f8106cab271f10a916dfade9a0d597ea11ccf40211fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-10-07T11:10:16Z",
    "title_canon_sha256": "5ddc544e10dbb21159ca93f1b7c64f6d7897fcedb410e1e7fdd41551aa31cf50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1484",
    "kind": "arxiv",
    "version": 1
  }
}