Pith Number

pith:OGKYW4LQ

pith:2011:OGKYW4LQYKH7C574Y66F76RDFT

not attested not anchored not stored refs pending

Fourier Transform Representation of the Extended Fermi-Dirac and Bose-Einstein Functions with Applications to the Family of the Zeta and Related Functions

Asghar Qadir, Asifa Tassaddiq

arxiv:1104.4346 v1 · 2011-04-21 · math-ph · math.CA · 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{OGKYW4LQYKH7C574Y66F76RDFT}

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	2026-05-18T04:23:34.817358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71958b7170c28ff177fcc7bc5ffa232cdeec5794fadf9c1c326f9f52d856fe60

Aliases

arxiv: 1104.4346 · arxiv_version: 1104.4346v1 · doi: 10.48550/arxiv.1104.4346 · pith_short_12: OGKYW4LQYKH7 · pith_short_16: OGKYW4LQYKH7C574 · pith_short_8: OGKYW4LQ

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/OGKYW4LQYKH7C574Y66F76RDFT \
  | 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: 71958b7170c28ff177fcc7bc5ffa232cdeec5794fadf9c1c326f9f52d856fe60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82bfeddef822832aa6c032ffeda942bce11f8b605f954fc0ef73a3c149377a1f",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-04-21T18:58:34Z",
    "title_canon_sha256": "ea8e2fe8969fa9874cb64344e7e190ee05609bdb76805d26e0316bf56428f94d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4346",
    "kind": "arxiv",
    "version": 1
  }
}