Pith Number

pith:G4I25X5D

pith:2011:G4I25X5DF3A3PNFYIZ4UZKFU42

not attested not anchored not stored refs pending

Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications

Yilmaz Simsek

arxiv:1111.3848 v2 · 2011-11-16 · 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{G4I25X5DF3A3PNFYIZ4UZKFU42}

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	2026-05-18T00:00:37.437935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3711aedfa32ec1b7b4b846794ca8b4e6841e1ce595ff69a7a46380d8d7a4c82a

Aliases

arxiv: 1111.3848 · arxiv_version: 1111.3848v2 · doi: 10.48550/arxiv.1111.3848 · pith_short_12: G4I25X5DF3A3 · pith_short_16: G4I25X5DF3A3PNFY · pith_short_8: G4I25X5D

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/G4I25X5DF3A3PNFYIZ4UZKFU42 \
  | 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: 3711aedfa32ec1b7b4b846794ca8b4e6841e1ce595ff69a7a46380d8d7a4c82a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5384c7f357fa8c9a1ebaa315281c5029a0787282ff8cc73d2aa1f532cfb2e196",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-11-16T16:11:41Z",
    "title_canon_sha256": "ef360ac6bd5f0b24eaf8930e5c642287d1283ebf43d47e3a00806608fddc448a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3848",
    "kind": "arxiv",
    "version": 2
  }
}