Pith Number

pith:2IHENLPR

pith:2018:2IHENLPRSQ6RYO6BQ5ZBMWRSFG

not attested not anchored not stored refs pending

The generalized modified Bessel function $K_{z,w}(x)$ at $z=1/2$ and Humbert functions

Rahul Kumar

arxiv:1810.03093 v1 · 2018-10-07 · 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{2IHENLPRSQ6RYO6BQ5ZBMWRSFG}

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	2026-05-18T00:03:54.539637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d20e46adf1943d1c3bc18772165a3229bcf487b142426e99e2406eaf5cc3a222

Aliases

arxiv: 1810.03093 · arxiv_version: 1810.03093v1 · doi: 10.48550/arxiv.1810.03093 · pith_short_12: 2IHENLPRSQ6R · pith_short_16: 2IHENLPRSQ6RYO6B · pith_short_8: 2IHENLPR

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/2IHENLPRSQ6RYO6BQ5ZBMWRSFG \
  | 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: d20e46adf1943d1c3bc18772165a3229bcf487b142426e99e2406eaf5cc3a222

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a65a036557a3781461c2791b43e6add286fd55addbed874e36736c8f78b024ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-10-07T06:54:07Z",
    "title_canon_sha256": "82cd8a759f07b28ffab4e2a5ef4b975125773dead678c736c47c67bfe2a8b5df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.03093",
    "kind": "arxiv",
    "version": 1
  }
}