Pith Number

pith:TDEICF4L

pith:2016:TDEICF4LVAH3PLIWVIYOLZTRWT

not attested not anchored not stored refs pending

Generalized Huygens types inequalities for Bessel and modified Bessel functions

Khaled Mehrez

arxiv:1601.01007 v1 · 2016-01-05 · 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{TDEICF4LVAH3PLIWVIYOLZTRWT}

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	2026-05-18T01:23:18.235797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98c881178ba80fb7ad16aa30e5e671b4ed61753693af6e83ae66a4b3797d6893

Aliases

arxiv: 1601.01007 · arxiv_version: 1601.01007v1 · doi: 10.48550/arxiv.1601.01007 · pith_short_12: TDEICF4LVAH3 · pith_short_16: TDEICF4LVAH3PLIW · pith_short_8: TDEICF4L

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/TDEICF4LVAH3PLIWVIYOLZTRWT \
  | 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: 98c881178ba80fb7ad16aa30e5e671b4ed61753693af6e83ae66a4b3797d6893

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bb22cea56aa5ed1ae3875063341b8bcec854a868c9687851c23ecebb5e4ccac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-01-05T22:41:00Z",
    "title_canon_sha256": "41f6431306928a077ad3bf7bc80b9ea85c58e9bf08eb4ddbf0766bb85ebe9b69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.01007",
    "kind": "arxiv",
    "version": 1
  }
}