Pith Number

pith:AZHYJLGJ

pith:2011:AZHYJLGJFQ4UXQ3E6ICJ4WSB5M

not attested not anchored not stored refs pending

A Remarkable Identity Involving Bessel Functions

Diego E. Dominici, Peter M.W. Gill, Taweetham Limpanuparb

arxiv:1103.0058 v1 · 2011-03-01 · math.CA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AZHYJLGJFQ4UXQ3E6ICJ4WSB5M}

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	2026-05-18T02:44:57.138137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

064f84acc92c394bc364f2049e5a41eb01b345c5bb1c65e2e80e92bec0e3c3ab

Aliases

arxiv: 1103.0058 · arxiv_version: 1103.0058v1 · doi: 10.48550/arxiv.1103.0058 · pith_short_12: AZHYJLGJFQ4U · pith_short_16: AZHYJLGJFQ4UXQ3E · pith_short_8: AZHYJLGJ

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/AZHYJLGJFQ4UXQ3E6ICJ4WSB5M \
  | 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: 064f84acc92c394bc364f2049e5a41eb01b345c5bb1c65e2e80e92bec0e3c3ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e87d1219d23632923752b8b284209249d34871023d5d991cbea379d0a69214fb",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-03-01T00:56:08Z",
    "title_canon_sha256": "9291ee09d6857ca3c3bf1fff4af1a751eafaddd279fc2d742abb1445ed89e67f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0058",
    "kind": "arxiv",
    "version": 1
  }
}