Pith Number

pith:6IVXYDUA

pith:2013:6IVXYDUAELSDOK32UQKFNDKMTV

not attested not anchored not stored refs pending

Products of Bessel functions and associated polynomials

E. Di Palma, E. Sabia, G. Dattoli, S. Licciardi

arxiv:1311.1705 v3 · 2013-11-07 · 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{6IVXYDUAELSDOK32UQKFNDKMTV}

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	2026-05-17T23:43:43.627956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f22b7c0e8022e4372b7aa414568d4c9d6c5d82f0db6cad78d189b46b20f96ecf

Aliases

arxiv: 1311.1705 · arxiv_version: 1311.1705v3 · doi: 10.48550/arxiv.1311.1705 · pith_short_12: 6IVXYDUAELSD · pith_short_16: 6IVXYDUAELSDOK32 · pith_short_8: 6IVXYDUA

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/6IVXYDUAELSDOK32UQKFNDKMTV \
  | 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: f22b7c0e8022e4372b7aa414568d4c9d6c5d82f0db6cad78d189b46b20f96ecf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ed213691ae204389ee43a7b17f41b079bbaa5e975617e3c06dd6b9a7596efb4",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-11-07T14:58:40Z",
    "title_canon_sha256": "c8b036dab97e39ce9cf9bceebc310a6713e1f3dda5e38c830fa9491dbb7732e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1705",
    "kind": "arxiv",
    "version": 3
  }
}