Pith Number

pith:FOCMXBCD

pith:2015:FOCMXBCD5PAZNI3HQLC7HZIXZE

not attested not anchored not stored refs pending

Asymptotic expansion of the risk of maximum likelihood estimator with respect to $\alpha$-divergence as a measure of the difficulty of specifying a parametric model -- with detailed proof

Yo Sheena

arxiv:1510.08226 v10 · 2015-10-28 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FOCMXBCD5PAZNI3HQLC7HZIXZE}

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	2026-05-18T00:03:37.579854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b84cb8443ebc196a36782c5f3e517c90a5727e4e0730cfca731168965854746

Aliases

arxiv: 1510.08226 · arxiv_version: 1510.08226v10 · doi: 10.48550/arxiv.1510.08226 · pith_short_12: FOCMXBCD5PAZ · pith_short_16: FOCMXBCD5PAZNI3H · pith_short_8: FOCMXBCD

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/FOCMXBCD5PAZNI3HQLC7HZIXZE \
  | 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: 2b84cb8443ebc196a36782c5f3e517c90a5727e4e0730cfca731168965854746

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b74bb14ee77a146486467dccbfc407958ab6129b6c1f21d16c950865a0f71780",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2015-10-28T08:56:46Z",
    "title_canon_sha256": "f10e8991c7ed029adb1d63fc008736d9a97a3419d44c2d884324aae244ce003c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.08226",
    "kind": "arxiv",
    "version": 10
  }
}