Pith Number

pith:ZKET3G7T

pith:2011:ZKET3G7T2QR3OOC4G663DAAXRM

not attested not anchored not stored refs pending

On evaluation of integrals involving Bessel functions

D. Babusci, G. Dattoli

arxiv:1111.0881 v1 · 2011-11-03 · 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{ZKET3G7T2QR3OOC4G663DAAXRM}

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	2026-05-18T04:09:36.746000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca893d9bf3d423b7385c37bdb180178b1c139c327b641b69128e601bf55d49e4

Aliases

arxiv: 1111.0881 · arxiv_version: 1111.0881v1 · doi: 10.48550/arxiv.1111.0881 · pith_short_12: ZKET3G7T2QR3 · pith_short_16: ZKET3G7T2QR3OOC4 · pith_short_8: ZKET3G7T

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/ZKET3G7T2QR3OOC4G663DAAXRM \
  | 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: ca893d9bf3d423b7385c37bdb180178b1c139c327b641b69128e601bf55d49e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d0315285793cdf4bf4f320ae06b15712dee0ff1dd6d297fd29e84cfcd0b7664",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-11-03T15:35:34Z",
    "title_canon_sha256": "e749dbc50de34f3d9a4b13f76c6f384ab3fb0dfd0004b2e9e8bb3e604592dc39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0881",
    "kind": "arxiv",
    "version": 1
  }
}