Pith Number

pith:USOABXP2

pith:2019:USOABXP2NOIRQZJT2RC523DBFA

not attested not anchored not stored refs pending

A closed-form formula for the Kullback-Leibler divergence between Cauchy distributions

Frank Nielsen, Fr\'ed\'eric Chyzak

arxiv:1905.10965 v2 · 2019-05-27 · cs.IT · cs.SC · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{USOABXP2NOIRQZJT2RC523DBFA}

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	2026-05-17T23:44:53.541348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a49c00ddfa6b91186533d445dd6c6128357eecfdae9e311961d8ca0d197cee07

Aliases

arxiv: 1905.10965 · arxiv_version: 1905.10965v2 · doi: 10.48550/arxiv.1905.10965 · pith_short_12: USOABXP2NOIR · pith_short_16: USOABXP2NOIRQZJT · pith_short_8: USOABXP2

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/USOABXP2NOIRQZJT2RC523DBFA \
  | 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: a49c00ddfa6b91186533d445dd6c6128357eecfdae9e311961d8ca0d197cee07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec9335cb8ec4ff33c7e604c6c699289f04d4dfa738950b91d3692b1c8b027ecd",
    "cross_cats_sorted": [
      "cs.SC",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2019-05-27T04:05:17Z",
    "title_canon_sha256": "93d8d2db86f7aed1ead7764f95c8d3eff52925579925261a4d2779d1cf06de2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.10965",
    "kind": "arxiv",
    "version": 2
  }
}