Pith Number

pith:WBQD2DNW

pith:2014:WBQD2DNWWO3LGQJWLPCU6OG56E

not attested not anchored not stored refs pending

Expansion of Infinite Series Containing Modified Bessel Functions of the Second Kind

Guglielmo Fucci, Klaus Kirsten

arxiv:1411.7069 v1 · 2014-11-25 · math-ph · hep-th · 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{WBQD2DNWWO3LGQJWLPCU6OG56E}

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	2026-05-18T01:30:25.586074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0603d0db6b3b6b341365bc54f38ddf115f93a25b8d3b3ca92f372a43ae38bfa

Aliases

arxiv: 1411.7069 · arxiv_version: 1411.7069v1 · doi: 10.48550/arxiv.1411.7069 · pith_short_12: WBQD2DNWWO3L · pith_short_16: WBQD2DNWWO3LGQJW · pith_short_8: WBQD2DNW

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/WBQD2DNWWO3LGQJWLPCU6OG56E \
  | 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: b0603d0db6b3b6b341365bc54f38ddf115f93a25b8d3b3ca92f372a43ae38bfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd885f88d7890bfbc749fcbd02f83a2881170346206544128adf84238356ace8",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-11-25T23:45:31Z",
    "title_canon_sha256": "1cade530fdbeb34d916d848da8f40b41a8af2366960dee8179de44288b4b42ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.7069",
    "kind": "arxiv",
    "version": 1
  }
}