Pith Number

pith:VFCZXWZR

pith:2012:VFCZXWZRBU7NXA2FREKAW3KG52

not attested not anchored not stored refs pending

About some identities for Bessel polynomials

Christophe Vignat, Olivier L\'ev\^eque

arxiv:1210.2081 v1 · 2012-10-07 · math.FA · 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{VFCZXWZRBU7NXA2FREKAW3KG52}

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	2026-05-18T03:43:51.169191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9459bdb310d3edb834589140b6d46ee962aacd26ad298b4582cd6335cff991e

Aliases

arxiv: 1210.2081 · arxiv_version: 1210.2081v1 · doi: 10.48550/arxiv.1210.2081 · pith_short_12: VFCZXWZRBU7N · pith_short_16: VFCZXWZRBU7NXA2F · pith_short_8: VFCZXWZR

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/VFCZXWZRBU7NXA2FREKAW3KG52 \
  | 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: a9459bdb310d3edb834589140b6d46ee962aacd26ad298b4582cd6335cff991e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff7ee865fff5a688ccdedb7f785aa08ac9f6da1db704022aeaa14bbdc80e3700",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-10-07T17:33:50Z",
    "title_canon_sha256": "021334c3892d9cdd31189f406806f90c85297dea10f1fb0e82c26966b83a734b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2081",
    "kind": "arxiv",
    "version": 1
  }
}