Pith Number

pith:SPHZP3K2

pith:2010:SPHZP3K2UOMAEN6JUILUNAEYDR

not attested not anchored not stored refs pending

A new class of sum rules for products of Bessel functions

G. Bevilacqua, L. Moi, T. Mansour, V. Biancalana, Y. Dancheva

arxiv:1010.3623 v2 · 2010-10-18 · 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{SPHZP3K2UOMAEN6JUILUNAEYDR}

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	2026-05-18T03:14:39.498666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93cf97ed5aa3980237c9a2174680981c56b7c9c6a67bc412282badf4d11f3d4b

Aliases

arxiv: 1010.3623 · arxiv_version: 1010.3623v2 · doi: 10.48550/arxiv.1010.3623 · pith_short_12: SPHZP3K2UOMA · pith_short_16: SPHZP3K2UOMAEN6J · pith_short_8: SPHZP3K2

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/SPHZP3K2UOMAEN6JUILUNAEYDR \
  | 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: 93cf97ed5aa3980237c9a2174680981c56b7c9c6a67bc412282badf4d11f3d4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c98393b152fb59c05fff91ffc0c050765f9fd3ee6247d8194f5350f8ad12ef3",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-10-18T15:11:20Z",
    "title_canon_sha256": "fdcf4db8530464fec4cf1fdfd0ea24fb4df04ff57cff6bfefa7a31d30cd731f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3623",
    "kind": "arxiv",
    "version": 2
  }
}