Pith Number

pith:BCO6APO5

pith:2012:BCO6APO5OD2HEYYYEX6BDOILMY

not attested not anchored not stored refs pending

A function Class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions

Jamel El Kamel, Khaled Mehrez

arxiv:1205.1112 v1 · 2012-05-05 · 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{BCO6APO5OD2HEYYYEX6BDOILMY}

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	2026-05-18T03:56:12.082181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

089de03ddd70f472631825fc11b90b66372f8f899ec08d1db96246c304a55473

Aliases

arxiv: 1205.1112 · arxiv_version: 1205.1112v1 · doi: 10.48550/arxiv.1205.1112 · pith_short_12: BCO6APO5OD2H · pith_short_16: BCO6APO5OD2HEYYY · pith_short_8: BCO6APO5

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/BCO6APO5OD2HEYYYEX6BDOILMY \
  | 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: 089de03ddd70f472631825fc11b90b66372f8f899ec08d1db96246c304a55473

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdbd1c5477de989c1c4c4afad52c1905d8ae6918a7feaa73034e38eeb04570bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-05-05T08:22:29Z",
    "title_canon_sha256": "52089447c205cc2822271998cad54dc4fcbf346ee227737991a352a62339ed6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1112",
    "kind": "arxiv",
    "version": 1
  }
}