Pith Number

pith:KFJ7DIQI

pith:2016:KFJ7DIQID2LW2UNPY6MR2AP52F

not attested not anchored not stored refs pending

Certain unified integration formulas associated with generalized k-Bessel function

G. Rahman, K. S. Nisar, M. Arshad, S. Mubeen

arxiv:1612.08079 v1 · 2016-12-23 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KFJ7DIQID2LW2UNPY6MR2AP52F}

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	2026-05-18T00:54:04.965415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5153f1a2081e976d51afc7991d01fdd15475ac4f227d14814479d7b6b2e0d29b

Aliases

arxiv: 1612.08079 · arxiv_version: 1612.08079v1 · doi: 10.48550/arxiv.1612.08079 · pith_short_12: KFJ7DIQID2LW · pith_short_16: KFJ7DIQID2LW2UNP · pith_short_8: KFJ7DIQI

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/KFJ7DIQID2LW2UNPY6MR2AP52F \
  | 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: 5153f1a2081e976d51afc7991d01fdd15475ac4f227d14814479d7b6b2e0d29b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b063c94da6b7414a5ffa66d26886bd3b4c580f8974650930ef55d216b67974dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-12-23T20:21:07Z",
    "title_canon_sha256": "2ae7871b9bd8d43377dbd4570a07c52638abb1c9426ea47bafc0abbb3d6c7cea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08079",
    "kind": "arxiv",
    "version": 1
  }
}