Pith Number

pith:KRP25JVP

pith:2013:KRP25JVPKXDNWKCGVBTG6Z52S3

not attested not anchored not stored refs pending

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

Burkhard Zimmermann, Carsten Schneider, Christoph Koutschan, Manuel Kauers, Peter Paule, Stefan Gerhold

arxiv:1305.4818 v2 · 2013-05-21 · cs.SC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KRP25JVPKXDNWKCGVBTG6Z52S3}

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	2026-05-18T03:18:05.918390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

545faea6af55c6db2846a8666f67ba96f2b9b0483464aeea5c8f3612c82e6aa2

Aliases

arxiv: 1305.4818 · arxiv_version: 1305.4818v2 · doi: 10.48550/arxiv.1305.4818 · pith_short_12: KRP25JVPKXDN · pith_short_16: KRP25JVPKXDNWKCG · pith_short_8: KRP25JVP

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/KRP25JVPKXDNWKCGVBTG6Z52S3 \
  | 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: 545faea6af55c6db2846a8666f67ba96f2b9b0483464aeea5c8f3612c82e6aa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d869e6a674d007e1e649fcd40d445b6118e70807514f05e9240e57f150a00f78",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2013-05-21T13:53:11Z",
    "title_canon_sha256": "72e59f92f8bc802f24ea1aa21f18adca01572d09936b5ead52196d45592697b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4818",
    "kind": "arxiv",
    "version": 2
  }
}