Pith Number

pith:3OYXTNUO

pith:2013:3OYXTNUO55D5UTVHYUCOEDJ5HU

not attested not anchored not stored refs pending

Marcinkiewicz-Zygmund and ordinary strong laws for empirical distribution functions and plug-in estimators

Henryk Z\"ahle

arxiv:1301.0726 v1 · 2013-01-04 · 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{3OYXTNUO55D5UTVHYUCOEDJ5HU}

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	2026-05-18T03:37:17.821273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbb179b68eef47da4ea7c504e20d3d3d398458e278ebf3f3311434648361e47f

Aliases

arxiv: 1301.0726 · arxiv_version: 1301.0726v1 · doi: 10.48550/arxiv.1301.0726 · pith_short_12: 3OYXTNUO55D5 · pith_short_16: 3OYXTNUO55D5UTVH · pith_short_8: 3OYXTNUO

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/3OYXTNUO55D5UTVHYUCOEDJ5HU \
  | 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: dbb179b68eef47da4ea7c504e20d3d3d398458e278ebf3f3311434648361e47f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7ebd1abf4e8e0aab0f8e0cd03359266e67704764d213342617049a34afe635b",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-01-04T13:58:12Z",
    "title_canon_sha256": "c66c9a7c69ca1428666e5a5d039e1b6da1c4a3d475c57e5c002cf95d55f7872c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0726",
    "kind": "arxiv",
    "version": 1
  }
}