Pith Number

pith:5PSABUXH

pith:2011:5PSABUXHN6M72WJJYPIKXV3R3I

not attested not anchored not stored refs pending

Integrals of Bessel functions

B. Germano, D. Babusci, G. Dattoli, M. R. Martinelli, P. E. Ricci

arxiv:1110.6310 v1 · 2011-10-28 · 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{5PSABUXHN6M72WJJYPIKXV3R3I}

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	2026-05-18T04:09:57.078913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebe400d2e76f99fd5929c3d0abd771da2b5318e379f86ad8e3642c61c1dce006

Aliases

arxiv: 1110.6310 · arxiv_version: 1110.6310v1 · doi: 10.48550/arxiv.1110.6310 · pith_short_12: 5PSABUXHN6M7 · pith_short_16: 5PSABUXHN6M72WJJ · pith_short_8: 5PSABUXH

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/5PSABUXHN6M72WJJYPIKXV3R3I \
  | 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: ebe400d2e76f99fd5929c3d0abd771da2b5318e379f86ad8e3642c61c1dce006

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26bbaa89b8a5c97f99b92127f43fa42edecc82c1838c073d5e656f3f38d7b006",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-10-28T12:12:57Z",
    "title_canon_sha256": "24b50b748c28ea8bb7c37ab3833e7544bffcbc91cf3e5f47875c9b388dbc2f78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6310",
    "kind": "arxiv",
    "version": 1
  }
}