Pith Number

pith:EDSQZR4E

pith:2017:EDSQZR4ERW4MBDGQOW4QVUN3ME

not attested not anchored not stored refs pending

Inequalities for the modified Bessel function of the second kind and the kernel of the Kr\"{a}tzel integral transformation

Robert E. Gaunt

arxiv:1701.02978 v1 · 2017-01-11 · 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{EDSQZR4ERW4MBDGQOW4QVUN3ME}

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	2026-05-18T00:43:35.341558Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20e50cc7848db8c08cd075b90ad1bb61368e811b444556b8d5d93ee7aaa3fafc

Aliases

arxiv: 1701.02978 · arxiv_version: 1701.02978v1 · doi: 10.48550/arxiv.1701.02978 · pith_short_12: EDSQZR4ERW4M · pith_short_16: EDSQZR4ERW4MBDGQ · pith_short_8: EDSQZR4E

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/EDSQZR4ERW4MBDGQOW4QVUN3ME \
  | 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: 20e50cc7848db8c08cd075b90ad1bb61368e811b444556b8d5d93ee7aaa3fafc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2c0b6022a06a3d4e8c97ee7d49d3c7c7c0e85f8d4f03144c2d18e2ee4dad44d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-01-11T14:12:10Z",
    "title_canon_sha256": "f806adec91a295e28d416e91853fca35ac304828cc9b98e8763fff17ac8d859d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.02978",
    "kind": "arxiv",
    "version": 1
  }
}