Pith Number

pith:TCITH4X6

pith:2016:TCITH4X6KAHTCSPS3AZB4TEQPX

not attested not anchored not stored refs pending

Extension of Frame's type inequalities to Bessel and modified Bessel functions

Khaled Mehrez

arxiv:1603.04024 v1 · 2016-03-13 · 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{TCITH4X6KAHTCSPS3AZB4TEQPX}

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	2026-05-18T01:19:09.682673Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

989133f2fe500f3149f2d8321e4c907dd6ed0c61ad7eee77aeabf01c8c2fce0d

Aliases

arxiv: 1603.04024 · arxiv_version: 1603.04024v1 · doi: 10.48550/arxiv.1603.04024 · pith_short_12: TCITH4X6KAHT · pith_short_16: TCITH4X6KAHTCSPS · pith_short_8: TCITH4X6

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/TCITH4X6KAHTCSPS3AZB4TEQPX \
  | 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: 989133f2fe500f3149f2d8321e4c907dd6ed0c61ad7eee77aeabf01c8c2fce0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "accb58f6c9088e345bef67faeafb33f96ab8ee4d5ae5c45d50f41d36156ed84b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-03-13T12:39:20Z",
    "title_canon_sha256": "48c459769cc726d284fcd9e8580cd5d6b0201a01f6e073c9d96d6d2da392a434"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04024",
    "kind": "arxiv",
    "version": 1
  }
}