Pith Number

pith:ZCSIRM5G

pith:2019:ZCSIRM5GMS4VKEEC7LYBSWKAOG

not attested not anchored not stored refs pending

Special values of the Lommel functions and associated integrals

Bernard J. Laurenzi

arxiv:1901.03384 v1 · 2019-01-05 · 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{ZCSIRM5GMS4VKEEC7LYBSWKAOG}

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	2026-05-17T23:56:31.385371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8a488b3a664b9551082faf0195940719d1d8f1f509b89876d7d10ba16155c89

Aliases

arxiv: 1901.03384 · arxiv_version: 1901.03384v1 · doi: 10.48550/arxiv.1901.03384 · pith_short_12: ZCSIRM5GMS4V · pith_short_16: ZCSIRM5GMS4VKEEC · pith_short_8: ZCSIRM5G

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/ZCSIRM5GMS4VKEEC7LYBSWKAOG \
  | 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: c8a488b3a664b9551082faf0195940719d1d8f1f509b89876d7d10ba16155c89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcd3abe34d2bf0deb3759a1224fb7104df43484422d9f3afa484eb949c3de11e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-01-05T15:24:47Z",
    "title_canon_sha256": "beec856afed6a64597975698f2330812d48cfbe08cf63d71f553e735212f626a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.03384",
    "kind": "arxiv",
    "version": 1
  }
}