Pith Number

pith:6UKQ3AF6

pith:2007:6UKQ3AF6Z6JHFZCEWSE5XVYN4L

not attested not anchored not stored refs pending

Bessel functions of integer order in terms of hyperbolic functions

S. Cojocaru, V. B\^arsan

arxiv:math-ph/0703010 v2 · 2007-03-01 · 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{6UKQ3AF6Z6JHFZCEWSE5XVYN4L}

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	2026-05-18T01:09:15.657780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5150d80becf9272e444b489dbd70de2e602d2c2deb67c53d338b2a8e0ebc7bd

Aliases

arxiv: math-ph/0703010 · arxiv_version: math-ph/0703010v2 · doi: 10.48550/arxiv.math-ph/0703010 · pith_short_12: 6UKQ3AF6Z6JH · pith_short_16: 6UKQ3AF6Z6JHFZCE · pith_short_8: 6UKQ3AF6

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/6UKQ3AF6Z6JHFZCEWSE5XVYN4L \
  | 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: f5150d80becf9272e444b489dbd70de2e602d2c2deb67c53d338b2a8e0ebc7bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6446549bec97cac08db907ace476cf62b33d334dbe5b8ae53d899c844d6635f",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-03-01T15:20:18Z",
    "title_canon_sha256": "5996cde1aa99771db3bd6d31b637687298c67e9b7e363e6aa43b7f7a482c545e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0703010",
    "kind": "arxiv",
    "version": 2
  }
}